1 is 0.9999999999999............

[Undefined]

Can I ask? Were you a lawyer or solicitor in your working life? [ don't answer btw the question is only a joke]

Possibly legal reform would be more up your alley?

No worries. I will answer though, for the sake of 'completeness', hey?

Actually, in my long life as "troubleshooter" in diverse employment/research environments, I have used my curiosity about all the diverse fields of human and scientific endeavors, with a view to finding solutions to supposedly intractable problems. Many times I have saved an employer many hundreds of thousands by solving a problem which external consultants could not find. It is my nature and my pleasure to go and solve and simplify where others have just been exploiting elitism/reputation to get away with NOT solving a problem which can BE solved given application and intent TO solve objectively not for money or reputation but for its own sake and for the pleasure in solving seemingly complex/intractable situations for their own sake. That should, I trust, forestall any further wonderings, joking or otherwise, from any and all quarters and so allow concentrating on the points in discussion rather than the source, hey, QQ?

 

[Quantum Quack]

The following opinion, may be controversial to a lot of people but I will put it out there any way.
The thing to realize very clearly is that Mathematics IS NOT the study of logic, it is the application and "proving" ground of logic that is derived from the philosophical study of logic.
Your main concerns are philosophical in nature and not able to be dealt with by mathematics as mathematics is only interested in applying and proving the logic agreed to after philosophical consideration.
The main problem that I have found for my self is I often forget the above distinctions and like wise often get into enormous trouble for doing so.

Example:
0.999...= 1 is a mathematical equation derived from a certain philosophical school of thought that considers 1/infinity = 0 [ or so I tend to think at the moment ]

I think personally your points are valid enough to warrant serious philosophical discussion.

However attempting to bring them into currently held conventional mathematics would be and ultimately is, futile until the world of philosophy can agree with you.

Mathematicians generally are not philosophers. - the nature of your audience is very important.

 

[Quantum Quack]

Try this link and maybe lobby the fora admin to include a sub fora
Philosophy of Mathematics
then you can sit back and take a little license [flexibility] over how you approach your issues...
I might add most of the alternative theorist [so called crackpots and cranks, me included] at this fora are really discussing the philosophy of mathematics as mathematics, and that could be most of the problem.

 

[Tach]

And it is being pointed out to you that you are only trolling and making noise.

False, for the solution to the OP question see here.

 

[Quantum Quack]

No worries. I will answer though, for the sake of 'completeness', hey?

Actually, in my long life as "troubleshooter" in diverse employment/research environments, I have used my curiosity about all the diverse fields of human and scientific endeavors, with a view to finding solutions to supposedly intractable problems. Many times I have saved an employer many hundreds of thousands by solving a problem which external consultants could not find. It is my nature and my pleasure to go and solve and simplify where others have just been exploiting elitism/reputation to get away with NOT solving a problem which can BE solved given application and intent TO solve objectively not for money or reputation but for its own sake and for the pleasure in solving seemingly complex/intractable situations for their own sake. That should, I trust, forestall any further wonderings, joking or otherwise, from any and all quarters and so allow concentrating on the points in discussion rather than the source, hey, QQ?

I suggested that you not reply to the question but you have any way.

Years ago, before suffering a major and debilitating health issue, I was an employer, a managing director of a small company.
Having since worked and been sacked from a couple of multi national blue chips I know that this sort of expression would not make it past the front desk.

If I had to review an application or tender or referral review that was worded similar as your above post is worded it would have been rejected. If I had to do the same now I would like wise reject it.

I would be questioning what happened to someone who was/is obviously very clever to bring his ability to express himself down to such a "Non Commercial - Non-Professional" level.

I am writing the above because I know I am not the only one about to post or thinking of posting...regarding your expose' of your past career and vocation. Which, if founded is worthy of admiration. [and only you know the truth of it]

Apologies RC but someone has to say it....honestly with out flame...call it a reality check if you like...

Needless to say the above means little to the present situation.
As we can only go on what is before us.
Please read the pm sent

 

[Trippy]

Urmmm, Trippy, may I remind you that this is the "Alternative Theories" section, not the "Established Maths" section. Here participants are exploring and discussing alternative views with a view to further refining/replacing established understandings, if possible. Yes?

Some things can not be replaced because trying to do so leads to nonsense answers.

Regardless of the subforum you are in, If you can't handle having the rigour of your assertions challenged, pehaps you should simply leave sciforums. Or perhaps I should just permaban you now as the sockpuppet of a previously banned users.

Moreover, whenever the discussion is moved back to the very Axiomatic/Conventionality 'beginnings', and the reasons/validity/consistency OF those in the 'larger picture' context (and not being just constrained to 'blindly following' of the consequences OF those very same axioms/conventions once 'introduced'), then it is unavoidable to end up with WORDS to arrive at some sort of MUTUAL 'contextual understandings' rather than just being constrained to self-justifying circularity of just repeating the 'blindly following' numerical 'proofs' manipulations which depend on certain 'exceptions' in order to make the axioms/conventionality consistent in a self-serving way rather than exploring the basis for the whole system 'from scratch'.

The only circular logic is yourse. Those of us defending the position that 0.99(9) = 1 do not need to rely on fallacies.

And that is what I am doing (politely and 'alternatively' exploring/discussing) here certain claims made by you and others IN THE CONTEXT OF EXAMINING whence such claims arose and whether they are self-consistent in both the limited axioms AND in the 'bigger picture' which I have already made clear I am 'coming from' in this discussion.

Still not a good reason to post word salad.

Given this section, and the nature of the discussion as I point out, it is a bit ungenerous to characterize the INESCAPABLE USE of EXPLORATORY and necessary WORDS and discussion modes which must necessarily precede any 'blindly following' and 'self-serving' REPETITION of 'numerical proofs' and all those very things which this discussion (from where I am coming) are all in question precisely because of the 'from scratch' exploration/discussion points/words presented to treat what went before the axioms/conventions rather than just what follows them (which we all agree DOES blindly follow 'given' those axioms/conventions, but which I now question the 'completeness' of those axioms/conventions THEMSELVES).

The failure is not in the axioms, but your ability to understand them.

So your ungenerous and 'personal' attitude characterizing others use (perforce of the nature of this discussion) of their polite and on-topic descriptive words in fair context, as 'word salad', is not really playing cricket, is it. It brings a certain prejudicial air to your reading in the context, which only makes the common understanding part of a conversation difficult from the very start, and failure to fully understand the other guys' stance AS EXPLAINED in their (so-called by you) 'word salad' indicates laziness and/or reading bias and automatic resort to kneejerking rather than fair and exhaustive conversation on point as presented/explained in context. Yes?

No. What it means is that reading your posts is, at times, bordering on physically painful. What it means is that you have just wasted three paragraphs essentially restating the same thing. What it means is that you seem incapable of succinctness.

If you do not read this reply like many others) properly and fairly, then you automatically disqualify yourself from, and maybe even distort, the conversation based on your own personal attitudes to 'the source' rather than fairly and considering the points put in context of THIS Alternative Theories section/discussion. Yes?

No, and now you're just being vacuuous. What's more is you've just wasted five whole paragraphs complaining without either making a valid point relevant to the discussion or in response to anything I raised.

With respect, but you seem not to have read or understood my quoted statement (to Pete) recognizing the differences IN CONTEXT.

I have, repeatedly, I read it several times until my eyes started bleeding, my sould cried out in agony and my braincells started committing mass suicide.

If you had read/understood properly, then you would have gathered that I said zeros can be trivial in some cases and not trivial in other cases. Context indicates there significance or their non-significance etc. That is what I said. So your attempt at characterizing that I did not recognize/understand the difference is sailing pretty close to a 'strawman'. But perhaps it isn't meant to be a strawman; perhaps you just didn't read/understand that relevant post/comment properly and IN FULL. I will assume so rather than take it as an intentional strawman (since I know you would never do such a thing intentionally).

The only strawman is yours. Here's what you haven't understood. Zero is never trivial. You have made a bare assertion, you have done nothing to defend that assertion, and I am challenging it by pointing out that significance is not the same thing as triviality.

Do you get it yet, or do you want me to carve it into your forehead witha coal chisel?

There is no such thing as a trivial zero. There is only significant zeroes and the conventions revolve around whether or not we write them. Just because we agree not to write them doesn't make them Trivial, nor does it mean they cease to exist.

Ok. Conventions. Let's assume (for the sake of argument) that I agree with your insistence on a "pre-existing zeros" convention; ie:

"0.00000 ->" in an unending series of 'pre-existing' zeros to the right of the decimal point. Where do we get to with that convention?

Because that's what numbers are. This is primary school mathematics.
When we write 0 what we mean is that we have:

$$0 \times 10^n + 0\times10^{n-1} + 0\times10^{n-2} + ... + 0\times10^3 + 0\times 10^2 + 0\times 10^1 + 0\times10^0 + 0\times10^{-1} + 0\times10^{-2} + ... 0\times10^{-n}$$

That's where the zeroes come from - they denote that there is no contribution from that power of 10

The example I initially questioned, IN THAT CONTEXT only,was Pete's use of a 'proof' involving the step/operation :

10 x 0.99999... = 9.9999...

I pointed out that fundamentally we added the zero from the 10 to the end of the original 0.9999... unending string, which "forced" the unending string to move the leading "9" one position to the left, past the decimal point, resulting in:

9.9999...0

No we didn't. You can't add something onto the end of something else that is unending. What you've stated is a nonsense. Take a moment to think about it.

Consider applying your 'logic' as follows:
$$\frac{1}{9} = 0.1111(1)$$
$$\frac{1}{9} \times 10 = 0.1111(1) \times 10$$
$$\frac{10}{9} = 1.111(1)0$$
$$1\frac{1}{9} - 1= 1.111(1)0 - 1$$
$$\frac{1}{9} = 0.111(1)0$$
Which can only be interpreted as a contradiction. Your methodology leads to a contradiction, mine does not. Your methodology is wrong, mine is right.

Pete's 'convention' was to interpret that 'result' as being the (in my view TRIVIAL convention) "action" of "shifting the decimal point to the right".

Pete's 'convention' is correct, yours is wrong, it leads to a contradiction, also consider:
$$ 0.001 \times 10 = 0.01$$
There is no zero added anywhere, so not only does your 'convention' lead to a contradiction, it also fails to account for all cases.

The reason why the decimal is shifted to the right when we multiply by ten goes back to this:
$$0 \times 10^n + 0\times10^{n-1} + 0\times10^{n-2} + ... + 0\times10^3 + 0\times 10^2 + 0\times 10^1 + 0\times10^0 + 0\times10^{-1} + 0\times10^{-2} + ... 0\times10^{-n}$$
When we multiply by ten, we increase the power by one, which effectively shifts the decimal to the right, and so if you consider 12.34:
$$1\times10^1 + 2\times 10^0 + 3 \times 10^{-1} + 4 \times 10^{-2}$$
It becomes:
$$1\times10^2 + 2\times 10^1 + 3 \times 10^{0} + 4 \times 10^{-1}$$
or 123.4 (again, another situation where there is no zero added).

Whereas I argued the "alternative" view (from observation of the real fundamentals I perceive); ie:

That in fact the REAL action was to add a zero (from the real number 10 factor/operation/entity) to the end of the unending string, and so by that actual action forced the ACTUAL NUMBER leading 9 to move to the left, rather than merely trivially and conventionally making some NON-real "action/operation" trivially described as "moving the decimal point to the right".

Your 'alternative' view leads to contradictions and fails to account for all cases.

If zero is a number; and if that zero IN CONTEXT IS 'significant' and not just trivial, THEN I merely observe that the 'real action involving that adding a zero at the end is MORE fundamental and significant than any mere convention of "moving the decimal point to the right" as per his argument/proof in that case/context.

There you go on that trivial bender again. Once again, your alternative view leads to contradictions and fails to account for all cases.

Oh, and before you come back with the obvious trivial retort that 'the pre-existing zeros' and 'the repeating 9 string never 'ends', you would be trying to have it both ways: ie, such strings are conventionally presumed (via the Limits argument) to END at some limiting 'state' in the context of 'infinity' arguments/conventions; and yet you adjured QQ to "try long division" etc which never ends. So I leave it to the more 'real action' context to tell which 'take' is the real way to understand this aspect being re-examined in this 'alternative theory' section/discussion.

Word salad. Would you like some cheese with that?

They're infinite. They never end. A limit is something that is approached but never reached. It doesn't matter how many times you divide three into 10, the answer is always going to be the same, 3 with 1 remainder.

Anyhow, that's it, that's where I am coming from in this discussion of alternative exploration 'from scratch' context, mate. No more, no less than that. If it's still all 'word salad' to you, or if you don't bother reading all the arguments in full, then you leave yourself open to creating further UNINTENTIONAL 'strawmen'.

Right, because clearly if your posts are word salad, it's my fault, and if I disagree with you it's obviously because I haven't read them, right?

It couldn't possibly be because of what you've written, could it?

 

[Undefined]

Hi QQ.

Sorry for not answering right away, I had to leave for a while. Still not much time, so briefly...

I suggested that you not reply to the question but you have any way.

Years ago, before suffering a major and debilitating health issue, I was an employer, a managing director of a small company.
Having since worked and been sacked from a couple of multi national blue chips I know that this sort of expression would not make it past the front desk.

If I had to review an application or tender or referral review that was worded similar as your above post is worded it would have been rejected. If I had to do the same now I would like wise reject it.

I would be questioning what happened to someone who was/is obviously very clever to bring his ability to express himself down to such a "Non Commercial - Non-Professional" level.

I am writing the above because I know I am not the only one about to post or thinking of posting...regarding your expose' of your past career and vocation. Which, if founded is worthy of admiration. [and only you know the truth of it]

Apologies RC but someone has to say it....honestly with out flame...call it a reality check if you like...

Needless to say the above means little to the present situation.
As we can only go on what is before us.
Please read the pm sent

Like I said, I chose to answer it for the sake of 'completeness' and to help dispel certain 'urban legends' regarding my motives etc etc., by again reminding everyone that I come at all these matters from the perspective of one who, since age 9, has remained an independent and objective atheist and scientist/researcher in practically all disciplines over the years since to my present 64 years.


And I would draw your attention to the fact that my reply was not in the context of 'Job Application' or any other context except for clarification as to where I have been coming from OBJECTIVELY on the issues I comment on in this thread context. So I don't see the relevance of your treating it in the context of a job application which would have to survive 'coming across your front desk' as employer in whatever business you were in. Fair objection to your out-of-context characterization of my post there?

Anyhow, I certainly took no offense at your question, mate. And explained in the PM responding to yours the reasons why I chose to answer it of my own free will. So no problem; we're good, yes QQ?

The following opinion, may be controversial to a lot of people but I will put it out there any way.
The thing to realize very clearly is that Mathematics IS NOT the study of logic, it is the application and "proving" ground of logic that is derived from the philosophical study of logic.
Your main concerns are philosophical in nature and not able to be dealt with by mathematics as mathematics is only interested in applying and proving the logic agreed to after philosophical consideration.
The main problem that I have found for my self is I often forget the above distinctions and like wise often get into enormous trouble for doing so.

Example:
0.999...= 1 is a mathematical equation derived from a certain philosophical school of thought that considers 1/infinity = 0 [ or so I tend to think at the moment ]

I think personally your points are valid enough to warrant serious philosophical discussion.

However attempting to bring them into currently held conventional mathematics would be and ultimately is, futile until the world of philosophy can agree with you.

Mathematicians generally are not philosophers. - the nature of your audience is very important.

The following opinion, may be controversial to a lot of people but I will put it out there any way.
The thing to realize very clearly is that Mathematics IS NOT the study of logic, it is the application and "proving" ground of logic that is derived from the philosophical study of logic.
Your main concerns are philosophical in nature and not able to be dealt with by mathematics as mathematics is only interested in applying and proving the logic agreed to after philosophical consideration.
The main problem that I have found for my self is I often forget the above distinctions and like wise often get into enormous trouble for doing so.

Example:
0.999...= 1 is a mathematical equation derived from a certain philosophical school of thought that considers 1/infinity = 0 [ or so I tend to think at the moment ]

I think personally your points are valid enough to warrant serious philosophical discussion.

However attempting to bring them into currently held conventional mathematics would be and ultimately is, futile until the world of philosophy can agree with you.

Mathematicians generally are not philosophers. - the nature of your audience is very important.

Did you catch my post #258, where I expressly pointed that I was in reality doing the exact opposite, and that it is the current mathematician practice to mix in the philosophical when it suits them to gloss over the fundamentals I am trying to highlight (in this discussion context only)? Here it is again, quoted, in a nutshell...

...

See? It is not I introducing philosophical concepts into the mathematics construct; in fact , all, my arguments so far have been directed at trying to REMOVE the need for such LIMITS, Undefined, Infinity philosophical concepts that have ALREADY been introduced BY the mathematicians into the mathematics.

Is that understood correctly now as to where I am coming from, and not as you've just inadvertently implied, incorrectly, having full regard to what has transpired from my end so far?

Cheers mate!

 

[Undefined]

Hi Trippy.

Before proceeding to reply item by item, please have regard to what you may have mssied regarding the question of context when treating zeros as trivial or not etc...

rpenner posted this short comment to QQ, and I noted it accordingly in my post #244 which I wish you would read (despite the pain you say you suffer when reading me) at least what rpenner had to say IN THIS CONTEXT, so that we do not continue cross-purpose exchanges on things which have been clarified by others already; here is the relevant section of that post #244...

Thereby eliminating the need to consider the decimal positions which hold zeros, which are all of them to the right of the decimal point.

Ok? Let's proceed...

Some things can not be replaced because trying to do so leads to nonsense answers.

I already quite clearly and often and categorically point out that I am NOT "trying to replace" anything; rather I am trying to REMOVE philosophical add-ons (Infinity, Limits arguments based on same, and "undefined" results and trivial 'proofs' etc) FROM in the mathematics which the mathematicians introduce whenever the INCOMPLETENESS of the axioms/assumptions used are not sufficient to AVOID these philosophical mix-ins and inevitable undefined dead-end excuses for NOT being complete. That the current maths is not complete is agreed by all, isn't it?

Regardless of the subforum you are in, If you can't handle having the rigour of your assertions challenged, pehaps you should simply leave sciforums. Or perhaps I should just permaban you now as the sockpuppet of a previously banned users.

First of all, in this Alternative Theories section the latitude is great to DEVELOP one's position because it IS an alternative perspective not already embued with the 'common understandings' which the 'established' conventional system has accumulated over many decades. So your DEMAND for IMMEDIATE complete and exhaustive presentation is not really fair, is it? Even Einstein, even with the maths of the time, had to wait decades for exhaustive DEVELOPMENT of his NEW perspective. Yes?

So please mate, let's have less of the 'elitist' and 'exclusionary pre-emption' tactics designed to intimidate (backed up by unwarranted threats of 'banning', no less!), and more of the give and take until the discussion IS complete and exhausted in all aspects.

And for your information, the management have LONG been FULLY AWARE of who I am, and post with their express permission because the original banning was PROVEN to be the result of biased mod colluding with the troll who framed and baited etc until the colluders had an 'excuse' to ban the victim. So please get it straight once and for all: I was not the problem; it was the trolls and tactics aimed at banning unfairly (and your present intimidatory threat to ban just because YOU don't want to READ things properly is redolent of those bad old says when people were banned because of OTHERS (trolls and colluding mods) personal agendas and kneejerking using the excuse of 'crank' and 'word salad' etc even though you do not take the time to do due diligence to the preceding posts/contexts!

Give it a rest, Trippy, it won't work anymore as this site is much enlightened than it was in those bad old days when trolls and certain mods treated this site as their own personal realm to attack the person and ban from sheer spite and prejudice. Not a good look nowadays, mate.

The only circular logic is yourse. Those of us defending the position that 0.99(9) = 1 do not need to rely on fallacies.

No, you rely on trivial 'proofs' which I and others are already questioning. Whatever 'proofs' you bring it boils down to circuitous arguments essentially ultimately based on self-serving definitional conveniences designed to provide loopholes for when the incomplete axioms/maths hits an "undefined" or other "axiomatic non-sequitur" thus requiring the INTRODUCTION of PHILOSIPHICAL 'get out clauses/treatments to make it appear self-consistent when it is not. Hence the philosophically based INFINITY concept, the PHilosophically based LIMITS assumptions/interpretations instead of just proving that 0.99(9) etc etc without just moving the goal post back to some other equally non-sequitur assumption (like 0.111(1) argument etc etc) instead of a self-contained proof consistent and without the whole construct having "undefined" gaps.

Still not a good reason to post word salad.

Glib dismissal; and not worthy of a real scientist to use as an 'argument' which treats form as more important than the ideas to be objectively discussed irrespective of source or presentation in an INFORMAL discussion at an early stage of a new perspective being developed VIA such informal discussions. The 'crank' and the 'word salad' etc catch-cries in lieu of actual discussion is 'old hat' and should be consigned, as a 'debate' tactic/response, to the bin of all such meaningless trivialities and prejudicial debating styles.

The failure is not in the axioms, but your ability to understand them.

You and everyone agrees that the maths as is s not axiomatically complete YET. Yes? And I am reviewing those very axioms and trying to bring them back to fundamentals so that whatever incompleteness/undefined/philosophical inevitabilities that they have obviously 'built into' the current mathematics can be AVOIDED 'from scratch'. That is an approach to understanding the axioms AND making them better through review of the problems of philosophy/undefined etc dependence and of the trivial proofs which such 'fixes' result in, and which are themselves NOT to be used to 'justify' those SAME 'proofs' via self-serving circuitous 'fixes by definition' and philosophical 'outs' like Infinities and Limits and pre-determined 'definitions which ultimately refer back to themselves or some questionable 'fixes/inclusions' (as already mentioned).

No. What it means is that reading your posts is, at times, bordering on physically painful. What it means is that you have just wasted three paragraphs essentially restating the same thing. What it means is that you seem incapable of succinctness.

When someone says that they don't read properly (for whatever reason), then a truly objective person would DECLINE to comment, instead of proceeding to do so based on PARTIAL impressions of what is being argued by the other person (in however many ways and occasions, often necessitated precisely certain people do NOT read properly, for whatever their reasons, and they MISS the point made the first time...and instead just resort to "word salad" and "crank" characterization/framing to cover THEIR OWN failure to read and understand properly and fairly BEFORE making any comment at all).

No, and now you're just being vacuuous. What's more is you've just wasted five whole paragraphs complaining without either making a valid point relevant to the discussion or in response to anything I raised.

I have, repeatedly, I read it several times until my eyes started bleeding, my sould cried out in agony and my braincells started committing mass suicide.

Mate, would it surprise and/or upset you terribly if you were to learn that some people might experience a similar 'syndrome' from reading the constant repeating of textbook 'proofs' which keep missing the point that those 'proofs' are not valid if you miss the point being made by others which bring those 'axioms/proofs' into question (as already explained-----do I have to explain it again because YOU don't read properly 'because it hurts', and so keep missing the point and insisting on repeating YOUR 'proofs' which are NOT up to the task of answering the points raised in the counterview to your REPEATED ad nauseam 'trivial proofs' depending on philosophical 'fixes/mixes' etc as already pointed out)? Note you've just complained (again and again here and in previous posts), so what is good for the goose is good fro the gander, yes?

The only strawman is yours. Here's what you haven't understood. Zero is never trivial. You have made a bare assertion, you have done nothing to defend that assertion, and I am challenging it by pointing out that significance is not the same thing as triviality.

Do you get it yet, or do you want me to carve it into your forehead witha coal chisel?

There is no such thing as a trivial zero. There is only significant zeroes and the conventions revolve around whether or not we write them. Just because we agree not to write them doesn't make them Trivial, nor does it mean they cease to exist.


Because that's what numbers are. This is primary school mathematics.
When we write 0 what we mean is that we have:

$$0 \times 10^n + 0\times10^{n-1} + 0\times10^{n-2} + ... + 0\times10^3 + 0\times 10^2 + 0\times 10^1 + 0\times10^0 + 0\times10^{-1} + 0\times10^{-2} + ... 0\times10^{-n}$$

That's where the zeroes come from - they denote that there is no contribution from that power of 10

Please read again the opening clause above including rpenner's comment in that context. Thanks.

No we didn't. You can't add something onto the end of something else that is unending. What you've stated is a nonsense. Take a moment to think about it.

The context was the expression 10 x 0.999... = 9.999...as used by Pete and others; and the question of which is more fundamental, the convention based non-action of merely "moving the decimal formatting point to the right" OR the reality based action of the 10 x action bringing the zero to the 'end' of that ASSUMED 'unending string'?


I already pointed out in this, now excerpted/bolded, bit from my post #241 to you earlier:

...

Oh, and before you come back with the obvious trivial retort that 'the pre-existing zeros' and 'the repeating 9 string never 'ends', you would be trying to have it both ways: ie, such strings are conventionally presumed (via the Limits argument) to END at some limiting 'state' in the context of 'infinity' arguments/conventions; and yet you adjured QQ to "try long division" etc which never ends. So I leave it to the more 'real action' context to tell which 'take' is the real way to understand this aspect being re-examined in this 'alternative theory' section/discussion.

So it seems you didn't bother to read/understand that either. Or you wouldn't have come back with that complaint which I already expected and pointed out as unsatisfactory because it 'ants it both ways', as explained.

See how 'painful' it can also be for others?...to 'read' your repeated arguments that don't have regard to context and arguments that went before in this and other relevant exchange and so lead you to miss the point and just resort to repetition of off-the-shelf 'pre-fab' explanations/arguments? Other people can and do 'feel pain' when it comes to reading others posts too, but not all of them complain and let it get in the way of proper respectful interaction/attitude like you have been doing.

Consider applying your 'logic' as follows:
$$\frac{1}{9} = 0.1111(1)$$
$$\frac{1}{9} \times 10 = 0.1111(1) \times 10$$
$$\frac{10}{9} = 1.111(1)0$$
$$1\frac{1}{9} - 1= 1.111(1)0 - 1$$
$$\frac{1}{9} = 0.111(1)0$$
Which can only be interpreted as a contradiction. Your methodology leads to a contradiction, mine does not. Your methodology is wrong, mine is right.


Pete's 'convention' is correct, yours is wrong, it leads to a contradiction, also consider:
$$ 0.001 \times 10 = 0.01$$
There is no zero added anywhere, so not only does your 'convention' lead to a contradiction, it also fails to account for all cases.

The reason why the decimal is shifted to the right when we multiply by ten goes back to this:
$$0 \times 10^n + 0\times10^{n-1} + 0\times10^{n-2} + ... + 0\times10^3 + 0\times 10^2 + 0\times 10^1 + 0\times10^0 + 0\times10^{-1} + 0\times10^{-2} + ... 0\times10^{-n}$$
When we multiply by ten, we increase the power by one, which effectively shifts the decimal to the right, and so if you consider 12.34:
$$1\times10^1 + 2\times 10^0 + 3 \times 10^{-1} + 4 \times 10^{-2}$$
It becomes:
$$1\times10^2 + 2\times 10^1 + 3 \times 10^{0} + 4 \times 10^{-1}$$
or 123.4 (again, another situation where there is no zero added).


Your 'alternative' view leads to contradictions and fails to account for all cases.


There you go on that trivial bender again. Once again, your alternative view leads to contradictions and fails to account for all cases.


Word salad. Would you like some cheese with that?

They're infinite. They never end. A limit is something that is approached but never reached. It doesn't matter how many times you divide three into 10, the answer is always going to be the same, 3 with 1 remainder.


Right, because clearly if your posts are word salad, it's my fault, and if I disagree with you it's obviously because I haven't read them, right?

It couldn't possibly be because of what you've written, could it?

With regard to all your exercises and examples above, please refer to my previous comments above and previous posts, so that I won't have to repeat myself, either. Thanks.

Cheers and G'night, Kiwi!

 

[rpenner]

rpenner, Trippy, Pete, QQ have not produced any sound mathematical proofs to support their cases.

If they have, then show it here by induction.

By the definition of the limit of a sequence, every claim in this thread that a limit exists or has such-and-such a value is a statement of a theorem provable by induction. And since every statement in calculus about a derivative or integral existing is also a statement about a limit, it too is demonstrable by induction. So you are nit-picking because statements provable by induction are ubiquitous and if you look at [post=3126937]#201[/post], I specifically proved all my limits exist and what their values are in the section marked "Induction." But I didn't limit myself to just 0.999... but rather I handled all repeating decimal sequences which arise from two division algorithms and I didn't limit myself to just base-10 arithmetic either. If you are going to pull out the big guns, you might as well flatten the entire neighborhood.

So here we are, the proofs by induction that the recurrence relations of the division algorithms have their invariants obeyed for all values of n. And that leads directly to the proof of the statement $${a_0.a_1a_2a_3...}_b = \lim_{n\to\infty} z_n = \frac{p}{q} = \lim_{n\to\infty} z'_n = {a'_0.a'_1a'_2a'_3...}_b $$.

Induction
$$\forall n \in \mathbb{N}_0 \quad a_n, a'_n, s_n, s'_n \in \mathbb{N}_0 \; \wedge \; s_n < q \; \wedge \; s'_n \leq q \; \wedge \; z_n = \sum_{k=0}^{n} a_k b^{-k} \; \wedge \; z'_n = \sum_{k=0}^{n} a'_k b^{-k} \; \wedge \; b^n p = s_n + b^n q z_n \; \wedge \; b^n p = s'_n + b^n q z'_n
\forall n \in \mathbb{N} \quad a_n < b \; \wedge \; a'_n < b
p < b q \Rightarrow \forall n \in \mathbb{N}_0 \quad a_n < b \; \wedge \; a'_n < b$$

Thus
$$\forall n \in \mathbb{N}_0 \quad \frac{p}{q} \; - \; z_n \; = \; \frac{s_n}{q b^n} \\ \forall n \in \mathbb{N}_0 \quad \frac{p}{q} \; - \; z'_n \; = \; \frac{s'_n}{q b^n} \\ \forall n \in \mathbb{N}_0 \quad 0 \; \leq \; \frac{p}{q} \; - \; z_n \; < \frac{1}{b^n} \quad \wedge \quad 0 \; \leq \; \frac{p}{q} \; - \; z'_n \; \leq \frac{1}{b^n}$$

Limits
Since we define $$\sum_{k=0}^{\infty}$$ as $$ \lim_{n\to\infty}\sum_{k=0}^{n}$$ we have $$\sum_{k=0}^{\infty} a_k b^{-k} = \lim_{n\to\infty} z_n $$ and likewise for $$z'_n$$.

$$ \lim_{n\to\infty} z_n = \lim_{n\to\infty} z'_n = \frac{p}{q}$$
Thus both division algorithms deliver a valid sequence of digits that sum to the desired rational number.

So if you are going to ignore post #201, you are living in ignorance. But if you are claiming that I presented no proof, then you are living in denial.

Now way back in [post=3126184]post #72[/post] I wrote a proof by contradiction:

For all numbers, there is an number greater than that number. Because x + 1 > x.
1 is a number.
0.999... is a number.
If 0.999... = 1 then 1 - 0.999... = 0. But this is not what the OP assumes.

Our hypothesis must be 1 > 0.999.. from which the following follows:

If 1 > 0.999... then 1 - 0.999... > 0.
Define x = 1 - 0.999....
Then x is a number. And x > 0.
Then 1/x is a number. Therefore there is a number N > 1/x.

Therefore our hypothesis leads invariably to $$\exists N\quad N \gt \frac{1}{1 - \lim_{n \to \infty } \sum_{k=1}^{n} 9 \times 10^{-k} } = \lim_{n \to \infty } \frac{1}{1 - \sum_{k=1}^{n} 9 \times 10^{-k} } = \lim_{n \to \infty } \frac{1}{ 10^{-n} } = \lim_{n \to \infty } 10^n $$.

But no such N can exists, because there is always a value of M which makes the above untrue for all values of n > M. We can even write:
$$M = 1 + \lceil \log_{10} N \rceil$$ and prove
$$\forall n \geq M \quad N \not\gt 10^M \leq 10^n$$ .

​

Therefore the hypothesis that $$1 > 0.999...$$ cannot be true because 1 - 0.999... is smaller than any positive number.
Not even if N = $$(\textrm{1 googol})^{\tiny \textrm{1 googol}} = (10^{100})^{(10^{100})} = (10^{10^2})^{(10^{100})} = 10^{\left( 10^2 \times 10^{100} \right)} = 10^{10^{102}}$$ can we avoid this Archimedean property of numbers.
There is always a larger number -- the natural numbers are without bound.
And so $$M = 1 + \lceil \log_{10} 10^{10^{102}} \rceil = \textrm{100 googol} + 1$$

Your proof is invalid.

I think it is valid. Would you kindly point out one invalid link in the chain of logic I built?

When dealing with .9(n), you must proceed by some form of induction.

Well, I have in various ways. But just because I don't spell them out doesn't mean they aren't there. The strongest reliance on the principle of induction is in the statement $$\forall n \geq M \quad N \not\gt 10^M \leq 10^n$$ which is the uncontroversial result that repeated multiplying by 10 doesn't start getting smaller.

You will note under induction, you can't prove .9(n) is ever anything other than finite.

Under induction you can make various claims about the sequence 0.9, 0.99, 0.999, 0.9999, ... each of which only has a finite number of digits. To find the value of 0.999... where the digits never stop you need the concept of the limit of a sequence. But just as 0.9 = 1 - 1/10, 0.99 = 1 - 1/100, 0.999 = 1 - 1/1000 it follows that 0.999... must differ from 1 by a number smaller in magnitude than 1/N where N is any positive integer. The only such number in geometry or the real number system is zero.

In other words, see Kunen.

This is an authoritarian claim about a mathematical field you don't understand. Can't you at least cite the exact purported authoritative point?

But if I wanted to listen to your authority, I would use his text:

Given $$\mathbb{Q}$$ and its order, we define the real and complex numbers by:
Definition I.15.4 $$\mathbb{R}$$ is the set of all $$ x \in \mathcal{P}(\mathbb{Q})$$ such that $$x \neq \emptyset, \; x \neq \mathbb{Q}, \; $$ x has no largest element, and

$$ \forall p, q \in \mathbb{Q} \left[ p < q \in x \rightarrow p \in x \right ]$$.$$ \quad \quad \quad (*)$$​

$$\mathbb{C} = \mathbb{R} \times \mathbb{R}$$
Informally, if $$x \in \mathbb{R}$$, then one can define its lower Dedekind cut, $$C_{\tiny x} = \left{ q \in \mathbb{Q} : q < x \right} $$; then $$C_{\tiny x}$$ is a subset of $$\mathbb{Q}$$ satisfying (∗). Formally, we identify x with $$C_{\tiny x}$$ and simply define $$\mathbb{R}$$ to be the collection of all sets satisfying (∗). Of course, we have to define appropriate +, ·, and < on $$\mathbb{R}$$. Then, a complex number is a pair of reals $$\left<x, y\right>$$ (representing x + iy).

http://www.math.wisc.edu/~kunen/notes_post.ps The Foundations of Mathematics by Kenneth Kunen (October 29, 2007).
So according to this definition of the real numbers from Kunen, $$C_{\tiny 0.999...} = C_{\tiny 1}$$ because there is not a single rational number which is in one set and not the other (aka, there exists the smallest rational equal to or larger than 0.999... and it is 1). Therefore 0.999... = 1. Q.E.D.

In contrast with a lower Dedekind cut at a rational where $$C_{\tiny p/q}$$ has no largest element while the smallest element of $$\mathbb{Q} \backslash C_{\tiny p/q}$$ is $$\frac{p}{q}$$, both $$C_{\tiny \sqrt{2}}$$ has no largest element and $$\mathbb{Q} \backslash C_{\tiny \sqrt{2}}$$ has no smallest element. This is because $$\sqrt{2}$$ is irrational.

When handling finite ordinals, you must make all of your proofs by induction.

I doubt finite ordinals are relevant since 0.999... has more than any finite number of digits.

Here is a negative proof.

For all n, 1 - .9(n) has an infinite # of digits. Assume that is false. Find the least b such that 1 - .9(b) has an finite # of digits.

Then, .9(b) has an infinite number of digits, which is a contradiction.

So, a limit based on an ordinal sequence never reaches the limit.

Next time, try to use math and English to make a claim. Why should I care about the number of digits a value has? Digits are the number, they are just the representation of number in a convenient form. Counting digits tells you more about the choices made to represent the number in a certain media than about the number.

In base 2 I write "1100". In base 10 I write "12". In base 16 I write "C". Same number, different numbers of digits.

In your long post to QQ (post #220) , I have noted this because it effectively supports what I have been observing to Pete and Trippy et al about this aspect in the context so far...

The proof uses the multiplication of 0.999.... x 10 and then the subtraction of 0.999.... as a significant part of proving that 0.999... = 1

Thereby eliminating the need to consider the decimal positions which hold zeros, which are all of them to the right of the decimal point.

Precisely. The context is what affects the treatment of zeros, as I have been saying.

I disagree. I view a representation of a decimal number as a functional map from the set of integers $$\mathbb{Z}$$ into the set of the ten digits 0..9 subject to the condition that there exists a positive integer $$z_{\textrm{max}}$$ such that all places above that integer map to 0. Thus the number represented by the representation is $$\sum_{k\in\mathbb{Z}} d_k 10^k = \sum_{k=1}^{z_{\textrm{max}}} d_k 10^k + \sum_{k=0}^{\infty} d_{-k} 10^{-k} = \sum_{k=1}^{z_{\textrm{max}}} d_k 10^k + \lim_{n\to\infty} \sum_{k=0}^{n} d_{-k} 10^{-k}$$.

Now if there exists a non-positive $$z_{\textrm{min}}$$ such that all smaller digits are zero, it follows that
$$ \lim_{n\to\infty} \sum_{k=0}^{n} d_{-k} 10^{-k} = \sum_{k=0}^{-z_{\textrm{min}}} d_{-k} 10^{-k} + \lim_{n\to\infty} \sum_{k=1-z_{\textrm{min}}}^{n-z_{\textrm{min}}} d_{-k} 10^{-k} = \sum_{k=0}^{-z_{\textrm{min}}} d_{-k} 10^{-k} + \lim_{n\to\infty} \sum_{k=1-z_{\textrm{min}}}^{n-z_{\textrm{min}}} {\huge 0} = \sum_{k=0}^{-z_{\textrm{min}}} d_{-k} 10^{-k}$$
Which neatly avoids any need to prove that the limit converges. Zeros just make life easier.

I am assuming you DO agree that the current status quo of the mathematics system/construct IS incomplete?

Why would you assume you have the least notion what I think or that your use of the adjective "incomplete" is meaningful to an audience of pragmatic scientists or bookish philosophers let alone actual mathematicians? How can you declare mathematics "incomplete" until you have mastered all mathematics in existence? Argument from personal ignorance is a fallacy.
Of course there is a particular sense where mathematics must be incomplete, in that any self-consistent mathematical system cannot prove itself true. But I hardly think abandoning self-consistency for the "virtue" of a "proof" of "truth" is going to satisfy anyone. Principle of Explosion, and all that.

So why [do] you consider your opinion that 1 > 0.999... is a valid opinion even when the definition of real numbers says it is not and there are formal proofs of this on tertiary resources like Wikipedia and primary sources like the computer-validated proof at http://us.metamath.org/mpegif/0.999....html make it inescapable that the normal rules of math require 1 = 0.999...

If you want to invent new math to work with your expectations, you are welcome to try. But you don't get to win this debate which is based on the normal rules of math.

Repeating your naked assertions without argument of any kind is not a contribution to a dialogue or discussion; it's authoritarian posturing.

Richard Hamming "Mathematics on a Distant Planet." American Math Monthly 105 640-650 (1998)
"In mathematics we do not appeal to authority, but rather you are responsible for what you believe."​

Thus the burden is on you to either use the notation used by the rest of the world or take responsibility and actually explain what your notation means in detail

... you are depending on 'inescapable' rules

No need to distort what I was saying. I wasn't saying the rules were inescapable, I was saying that the rules are already adopted when the OP raises the question "does 0.999... equal 1?" and since the rules already answer this question (as Kunen shows, as us.metamath.com shows, as Wikipedia shows, etc) the conclusion is inescapable when you play by the agreed-upon rules.

Changing the rules is easy. In base 16, $${0.999...}_{16} = {0.6}_{10} < 1$$. Did this answer the question as posed? Of course not.

 

[Trippy]

Somebody show me where to stab repeatedlky to make Undefined's posts stop hurting?

 

[Quantum Quack]

Trippy, suggestion, switch to the Philosophy of Mathematics instead of mathematics and ask yourself:
Do I really want to discuss the Philosophy of Mathematics.
If not..then don't..

 

[Trippy]

Hi Trippy.

Before proceeding to reply item by item, please have regard to what you may have mssied regarding the question of context when treating zeros as trivial or not etc...

rpenner posted this short comment to QQ, and I noted it accordingly in my post #244 which I wish you would read (despite the pain you say you suffer when reading me) at least what rpenner had to say IN THIS CONTEXT, so that we do not continue cross-purpose exchanges on things which have been clarified by others already; here is the relevant section of that post #244...

On the one hand, i'm not generally in the habit of reading posts addressed to other people. On the other hand, I have read it, and it adds nothing.

Ok? Let's proceed...

Thereby eliminating the need to consider the decimal positions which hold zeros, which are all of them to the right of the decimal point.

I understand that thgis is your opinion. Your opinion is wrong, as I have demonstrated and tried to explain repeatedly.

I already quite clearly and often and categorically point out that I am NOT "trying to replace" anything; rather I am trying to REMOVE philosophical add-ons (Infinity, Limits arguments based on same, and "undefined" results and trivial 'proofs' etc) FROM in the mathematics which the mathematicians introduce whenever the INCOMPLETENESS of the axioms/assumptions used are not sufficient to AVOID these philosophical mix-ins and inevitable undefined dead-end excuses for NOT being complete. That the current maths is not complete is agreed by all, isn't it?

You're contradicting yourself. Here's what you said, the comment I was replying to:

Urmmm, Trippy, may I remind you that this is the "Alternative Theories" section, not the "Established Maths" section. Here participants are exploring and discussing alternative views with a view to further refining/replacing established understandings, if possible. Yes?

First of all, in this Alternative Theories section the latitude is great to DEVELOP one's position because it IS an alternative perspective not already embued with the 'common understandings' which the 'established' conventional system has accumulated over many decades.

Liar. That's not what I said.
I said that if you can't handle having the rigour of your assertions tested and challeneged you should leave. Even Einstein had his 'alternative theories' challenged and tested.

So your DEMAND for IMMEDIATE complete and exhaustive presentation is not really fair, is it? Even Einstein, even with the maths of the time, had to wait decades for exhaustive DEVELOPMENT of his NEW perspective. Yes?

Not what I said. Try responding to what I actually write in the future.

So please mate, let's have less of the 'elitist' and 'exclusionary pre-emption' tactics designed to intimidate (backed up by unwarranted threats of 'banning', no less!), and more of the give and take until the discussion IS complete and exhausted in all aspects.

They're not unwarranted, the rules in that regard are quite clear.

And for your information, the management have LONG been FULLY AWARE of who I am, and post with their express permission because the original banning was PROVEN to be the result of biased mod colluding with the troll who framed and baited etc until the colluders had an 'excuse' to ban the victim. So please get it straight once and for all: I was not the problem;

No, you are the problem. It takes two to tango buddy.

...it was the trolls and tactics aimed at banning unfairly (and your present intimidatory threat to ban just because YOU don't want to READ things properly is redolent of those bad old says when people were banned because of OTHERS (trolls and colluding mods) personal agendas and kneejerking using the excuse of 'crank' and 'word salad' etc even though you do not take the time to do due diligence to the preceding posts/contexts!

Yes, it's always everybody elses fault with you isn't it. Never yours.

Give it a rest, Trippy, it won't work anymore as this site is much enlightened than it was in those bad old days when trolls and certain mods treated this site as their own personal realm to attack the person and ban from sheer spite and prejudice. Not a good look nowadays, mate.

I'm not the one that needs to give it a rest. Look, you've just devoted, what are we at now? Three paragraphs? Responding to a sentence you could have just as easily ignored.

No, you rely on trivial 'proofs' which I and others are already questioning. Whatever 'proofs' you bring it boils down to circuitous arguments essentially ultimately based on self-serving definitional conveniences designed to provide loopholes for when the incomplete axioms/maths hits an "undefined" or other "axiomatic non-sequitur" thus requiring the INTRODUCTION of PHILOSIPHICAL 'get out clauses/treatments to make it appear self-consistent when it is not. Hence the philosophically based INFINITY concept, the PHilosophically based LIMITS assumptions/interpretations instead of just proving that 0.99(9) etc etc without just moving the goal post back to some other equally non-sequitur assumption (like 0.111(1) argument etc etc) instead of a self-contained proof consistent and without the whole construct having "undefined" gaps.

You have yet to actually demonstrate any of these.

What is it about the 0.11(1) argument that you don't like. Do you think that 1/9 is something other than 0.11(1)? Do you think that one remainder magically dissapears at some point? Nothing you have been presented with is circuitous or involves moving goalposts.

Glib dismissal; and not worthy of a real scientist to use as an 'argument' which treats form as more important than the ideas to be objectively discussed irrespective of source or presentation in an INFORMAL discussion at an early stage of a new perspective being developed VIA such informal discussions. The 'crank' and the 'word salad' etc catch-cries in lieu of actual discussion is 'old hat' and should be consigned, as a 'debate' tactic/response, to the bin of all such meaningless trivialities and prejudicial debating styles.

This... Doesn't even make any sense as a response.

Here's the context:

And that is what I am doing (politely and 'alternatively' exploring/discussing) here certain claims made by you and others IN THE CONTEXT OF EXAMINING whence such claims arose and whether they are self-consistent in both the limited axioms AND in the 'bigger picture' which I have already made clear I am 'coming from' in this discussion.

Still not a good reason to post word salad.

Arguing that something is nonsensical is perfectly valid.

You and everyone agrees that the maths as is s not axiomatically complete YET. Yes?

I've seen you make this assertion several times, I don't recall having seen anyone agree to it. You, seemingly, are still stuck on long division and what numbers actually mean, let alone how they're defined.

And I am reviewing those very axioms and trying to bring them back to fundamentals so that whatever incompleteness/undefined/philosophical inevitabilities that they have obviously 'built into' the current mathematics can be AVOIDED 'from scratch'.

How can you expect to review something which you manifestly do not understand? You're still trying to argue that the zeroes are trivial and not really there.

That is an approach to understanding the axioms AND making them better through review of the problems of philosophy/undefined etc dependence and of the trivial proofs which such 'fixes' result in, and which are themselves NOT to be used to 'justify' those SAME 'proofs' via self-serving circuitous 'fixes by definition' and philosophical 'outs' like Infinities and Limits and pre-determined 'definitions which ultimately refer back to themselves or some questionable 'fixes/inclusions' (as already mentioned).

They're only questionable in your head. I'm not going to improve brain surgery or rocket science by taking your approach and trying to redefine what a scalple is, am I?

When someone says that they don't read properly (for whatever reason), then a truly objective person would DECLINE to comment, instead of proceeding to do so based on PARTIAL impressions of what is being argued by the other person (in however many ways and occasions, often necessitated precisely certain people do NOT read properly, for whatever their reasons, and they MISS the point made the first time...and instead just resort to "word salad" and "crank" characterization/framing to cover THEIR OWN failure to read and understand properly and fairly BEFORE making any comment at all).

Liar.
I didn't say I haven't read it properly.

Mate, would it surprise and/or upset you terribly if you were to learn that some people might experience a similar 'syndrome' from reading the constant repeating of textbook 'proofs' which keep missing the point that those 'proofs' are not valid if you miss the point being made by others which bring those 'axioms/proofs' into question (as already explained-----do I have to explain it again because YOU don't read properly 'because it hurts', and so keep missing the point and insisting on repeating YOUR 'proofs' which are NOT up to the task of answering the points raised in the counterview to your REPEATED ad nauseam 'trivial proofs' depending on philosophical 'fixes/mixes' etc as already pointed out)? Note you've just complained (again and again here and in previous posts), so what is good for the goose is good fro the gander, yes?

You have yet to demonstrate a flaw in anything other than your understanding of the proofs. And once again, you're repeating the same lie. I didn't say that I haven't read your posts properly.

Please read again the opening clause above including rpenner's comment in that context. Thanks.

Please address the point actually being made. Thanks.

The context was the expression 10 x 0.999... = 9.999...as used by Pete and others; and the question of which is more fundamental, the convention based non-action of merely "moving the decimal formatting point to the right" OR the reality based action of the 10 x action bringing the zero to the 'end' of that ASSUMED 'unending string'?

I understand that, and what I have stated, repeatedly, is that your proofs of adding a zero to the end of the string are not only wrong, but they lead to nonsense answers and can not account for all of the observations.

I already pointed out in this, now excerpted/bolded, bit from my post #241 to you earlier:

Oh, and before you come back with the obvious trivial retort that 'the pre-existing zeros' and 'the repeating 9 string never 'ends', you would be trying to have it both ways: ie, such strings are conventionally presumed (via the Limits argument) to END at some limiting 'state' in the context of 'infinity' arguments/conventions; and yet you adjured QQ to "try long division" etc which never ends. So I leave it to the more 'real action' context to tell which 'take' is the real way to understand this aspect being re-examined in this 'alternative theory' section/discussion.

So it seems you didn't bother to read/understand that either. Or you wouldn't have come back with that complaint which I already expected and pointed out as unsatisfactory because it 'ants it both ways', as explained.

You're either a liar or an idiot - I responded directly to that

See how 'painful' it can also be for others?...to 'read' your repeated arguments that don't have regard to context and arguments that went before in this and other relevant exchange and so lead you to miss the point and just resort to repetition of off-the-shelf 'pre-fab' explanations/arguments? Other people can and do 'feel pain' when it comes to reading others posts too, but not all of them complain and let it get in the way of proper respectful interaction/attitude like you have been doing.

The fact that you don't like a fact or a response doesn't make that response wrong. Perhaps if you took the time to be more succinct and express yourself more clearly you would get further.

With regard to all your exercises and examples above, please refer to my previous comments above and previous posts, so that I won't have to repeat myself, either. Thanks.

Cheers and G'night, Kiwi!

Please actually addresss the points that have been raised. Thankyou.

 

[elte]

An important idea was touched upon earlier. 0.(9) is in a similar mathematical category as 7 because 7 can be considered shorthand for 7.(0)
The repeating zeroes confirms that the number hasn't been rounded. However, the decimal point and repeating 0s are normally omitted for convenience.

 

[Kittamaru]

Allow me to just ask this - Undefined / RealityCheck - who is it that has approved your stay here? Permanent bans are, well, just that... permanent. Please advise who we can corroborate your story with.

 

[Undefined]

Hi rpenner.

Thanks for your time and trouble in contributing to this discussion. Much appreciated.


I cannot see why you would take umbrage at my fairly pointing out that the current mathematics as a system is incomplete. Perhaps you (and everyone in this discussion could do with a fresh reminder regarding this fact? To that end, I refer you to the wiki on "Goedel's Incompleteness theorem":


In a nutshell, from the opening remarks of that wiki page:

Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic. The theorems, proven by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The two results are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible, giving a negative answer to Hilbert's second problem.

No more to be said about that, yes? Here is the link: http://en.wikipedia.org/wiki/Goedel's_theorem



I also note in your exchange with chinglu you make the leap from a straightforward number system argument to a philosophical statement which would have zero as a number which that statement can validly use to support its conclusion.

So, since much of the 'proofs' and arguments from conventional mathematics boil down to the question of how zero is to be treated in context, and all the other exchanges are therefore open to cross-purpose arguments until this question is put to bed, I will concentrate on this one aspect before any further cross-purpose misunderstandings arise because we are coming at this from entirely different perspectives. I quote, bold and highlight the statement in question...

Under induction you can make various claims about the sequence 0.9, 0.99, 0.999, 0.9999, ... each of which only has a finite number of digits. To find the value of 0.999... where the digits never stop you need the concept of the limit of a sequence. But just as 0.9 = 1 - 1/10, 0.99 = 1 - 1/100, 0.999 = 1 - 1/1000 it follows that 0.999... must differ from 1 by a number smaller in magnitude than 1/N where N is any positive integer. The only such number in geometry or the real number system is zero.

Earlier on, I presented to you the argument that your earlier statement about zero being neither positive nor negative supports my observation that in fact zero cannot BE on the number line and also BE neither positive nor negative. I pointed out that IF the zero point was at the beginning point of the positive arm of the number line, then that zero MUST be a positive number. Also, if the zero point was the first point on the negative arm of the number line, then that zero point MUST be a negative number. IF the extended number line (as your example "ring construct" symmetry implies) IS a CONTINUUM, then that would make zero BOTH positive AND negative, rather than what you claimed NEITHER positive NOR negative. Yes?

Hence my further observation to you at the time, that therefore zero is in reality an assumed 'balance state' or 'origin point' COMMON to both directions of the line construct. As such, then, 'zero point' is EFFECTIVELY another LABEL for A number which IS on the line BUT is merely A point like any other point anywhere else on that line (not in 'value' but in 'nature').

For example we construct an extended 'ring' number line DIVIDED arbitrarily at a point on the line where the BALANCE STATE between negative and positive direction MEET AT that balance point. So we LABEL it 'zero' OR 'origin' (as in the xyz co-ordinate construct) BUT the 'zero/origin' is labeled/treated as NEITHER positive NOR negative because it IS a number VALUE BALANCE point, not an VALUE ABSENCE point. Hence the zero in its context of balance/origin point, and not as a "unique number" which is currently treated as neither negative nor positive because the axioms are not contextually capable of distinguishing a zero which cannot be both negative and positive, and so must treat it by default as neither negative or positive.

Which leads to all the "undefined" problem. And also to the subtle and insidious introduction into the mathematics of further essentially PHILOSOPHICAL 'fixes' (and statements like that quoted and highlighted above) which, when examined closely and objectively, are also found to depend solely on philosophical concepts like INFINITY (this not a number either) and the LIMITS assumptions/constructs based on that infinity concept.

And hence why the mathematics as is currently developing from axioms that inherently include and depend on PHILOSOPHICAL 'fixes' (as I identified already above) and 'assumptive leaps' (like your one I quoted/highlighted above) which 'jumps' from number-line 'domain' to number 'definitions' (of zero) which exceed those 'domains'.

That's what I observe from the perspective I am coming from, bringing it all 'back to scratch' to see what can be done to make the axioms more 'contextually responsive and complete' from the 'word go'. It may upset some 'emotionally attached' types, but such personal considerations are not relevant to the objective review aimed at progressing both of the physics and the mathematics to a stage where the INcompleteness 'barrier' may be side-stepped by better formulation of the axioms/postulates so that they no longer depend on such philosophical 'fixes' and 'undefined' states/concepts as already mentioned.


Anyhow, thanks again sincerely for your time and trouble, rpenner. Cheers!

 

[Trippy]

An important idea was touched upon earlier. 0.(9) is in a similar mathematical category as 7 because 7 can be considered shorthand for 7.(0)
The repeating zeroes confirms that the number hasn't been rounded. However, the decimal point and repeating 0s are normally omitted for convenience.

Precisely one of the points that I have tried to make repeatedly to RealityCheck. The concept of moving the decimal point is not a matter of convenience or convention, it's a more accurate description of what is actually being done, especially when one considers what numbers actually represent.

But it seems RealityCheck doesn't like this and is unable to recognize that his insistence that what we're actually doing is 'adding on zeroes' fails to account for all cases and leads us to contradictions (and is therefore wrong). It's only true in a handfull of special cases.

 

[Undefined]

Hi Trippy.

elte
An important idea was touched upon earlier. 0.(9) is in a similar mathematical category as 7 because 7 can be considered shorthand for 7.(0)
The repeating zeroes confirms that the number hasn't been rounded. However, the decimal point and repeating 0s are normally omitted for convenience.

Precisely one of the points that I have tried to make repeatedly to RealityCheck. The concept of moving the decimal point is not a matter of convenience or convention, it's a more accurate description of what is actually being done, especially when one considers what numbers actually represent.

But it seems RealityCheck doesn't like this and is unable to recognize that his insistence that what we're actually doing is 'adding on zeroes' fails to account for all cases and leads us to contradictions (and is therefore wrong). It's only true in a handfull of special cases.

I already replied to that and pointed out that the convention has nothing to do with the action of multiplication ITSELF. That is why I observed to Pete about which is the more FUNDAMENTAL aspect, the convention to move a decimal point to the right", OR to bring the actual " tens" effect of the zero in "10 x 0.9999. =9.9999..." expression? Convention is NOT action, just a formatting convenience, as you say. There is a difference between fundamental actions and conventional conveniences of formatting.

Please ALL the relevant posts/exchanges on this aspect for the CONTEXT in which this observation was raised. Thanks.

On the one hand, i'm not generally in the habit of reading posts addressed to other people. On the other hand, I have read it, and it adds nothing.


I understand that thgis is your opinion. Your opinion is wrong, as I have demonstrated and tried to explain repeatedly.


You're contradicting yourself. Here's what you said, the comment I was replying to:



Liar. That's not what I said.
I said that if you can't handle having the rigour of your assertions tested and challeneged you should leave. Even Einstein had his 'alternative theories' challenged and tested.


Not what I said. Try responding to what I actually write in the future.


They're not unwarranted, the rules in that regard are quite clear.


No, you are the problem. It takes two to tango buddy.


Yes, it's always everybody elses fault with you isn't it. Never yours.


I'm not the one that needs to give it a rest. Look, you've just devoted, what are we at now? Three paragraphs? Responding to a sentence you could have just as easily ignored.


You have yet to actually demonstrate any of these.

What is it about the 0.11(1) argument that you don't like. Do you think that 1/9 is something other than 0.11(1)? Do you think that one remainder magically dissapears at some point? Nothing you have been presented with is circuitous or involves moving goalposts.


This... Doesn't even make any sense as a response.

Here's the context:


Arguing that something is nonsensical is perfectly valid.


I've seen you make this assertion several times, I don't recall having seen anyone agree to it. You, seemingly, are still stuck on long division and what numbers actually mean, let alone how they're defined.


How can you expect to review something which you manifestly do not understand? You're still trying to argue that the zeroes are trivial and not really there.


They're only questionable in your head. I'm not going to improve brain surgery or rocket science by taking your approach and trying to redefine what a scalple is, am I?


Liar.
I didn't say I haven't read it properly.


You have yet to demonstrate a flaw in anything other than your understanding of the proofs. And once again, you're repeating the same lie. I didn't say that I haven't read your posts properly.


Please address the point actually being made. Thanks.


I understand that, and what I have stated, repeatedly, is that your proofs of adding a zero to the end of the string are not only wrong, but they lead to nonsense answers and can not account for all of the observations.



You're either a liar or an idiot - I responded directly to that


The fact that you don't like a fact or a response doesn't make that response wrong. Perhaps if you took the time to be more succinct and express yourself more clearly you would get further.



Please actually addresss the points that have been raised. Thankyou.

Mate, what can I say? Perhaps it would be best if we ended our exchange instead of continuing in the vein you seem to be (whether intentionally or unintentionally) taking it?

I mean, you seem emotional rather than disinterestedly objective. You admit to being pained when reading others posts and to not reading other background relevant exchanges in the thread which may inform you better as to the actual stage of the discourse and so prevent you making inadvertent strawmen and cross-purpose replies etc. Add to all that 'personal' attitude the further threat as a mod in order to intimidate and to take advantage of your mod position/power to make obviously personally disparaging 'framings' and 'glib dismissals' and 'characterizations' like "crank" and "word salad" etc etc.

Now is that any way for a proper moderator on a good science site to behave nowadays? Ir is redolent of the past when trolls and compliant mods would collude for personal agendas to frame and ban people because they dared to question objectively and fairly discuss while being constantly baited and framed for banning by mods who behaved similarly (but worse then) to how you are behaving now.

You seem to be emotional and repetive in your glib 'proofs' which depend on similar glib assumptions all the way down the line irrespective which starting assumptions/expressions you have presented so far as 'counteragument' 'proof' examples.

You obviously miss the context and the proper implications because you admit you don't read others and read them emotionally (pained) when you do. You are obviously incapable of treating the issues raised with fairness and without bringing threats and intimidation as mod in order to force YOUR personal and emotive opinions/prejudices 'baggage' etc on others unconvinced by your replies so far.

It would be counter-productive to continue discussion here with you, Trippy, as you seem to be getting more personal, threatening and emotional as it goes on.

Therefore, mate, I humbly request you ignore my posts altogether and not respond in future, because your 'personal baggage' and 'emotionality' is neither good for objective discourse here nor good for your image/standing as mod here. Thanks anyway for your contribution/exchange so far, Trippy. Good luck in the future, and enjoy your objective science.maths discussions without all that emotion, mate. It's not good for the blood pressure! No hard feelings this end. See you round.

 

[Trippy]

Earlier on, I presented to you the argument that your earlier statement about zero being neither positive nor negative supports my observation that in fact zero cannot BE on the number line and also BE neither positive nor negative. I pointed out that IF the zero point was at the beginning point of the positive arm of the number line, then that zero MUST be a positive number. Also, if the zero point was the first point on the negative arm of the number line, then that zero point MUST be a negative number. IF the extended number line (as your example "ring construct" symmetry implies) IS a CONTINUUM, then that would make zero BOTH positive AND negative, rather than what you claimed NEITHER positive NOR negative. Yes?

Hence my further observation to you at the time, that therefore zero is in reality an assumed 'balance state' or 'origin point' COMMON to both directions of the line construct. As such, then, 'zero point' is EFFECTIVELY another LABEL for A number which IS on the line BUT is merely A point like any other point anywhere else on that line (not in 'value' but in 'nature').

0 = {}
1 = {0} = {{}}
2 = {0,1} = {{},{{}}}
3 = {0,1,2}
4 = {0,1,2,3}
5 = {0,1,2,3,4}
...
n = {0,1,2,3,4,5, ... , n-2, n-1}

 

[Undefined]

0 = {}
1 = {0} = {{}}
2 = {0,1} = {{},{{}}}
3 = {0,1,2}
4 = {0,1,2,3}
5 = {0,1,2,3,4}
...
n = {0,1,2,3,4,5, ... , n-2, n-1}

'Axiomatically', yes. But the whole discussion is about what that current axiomatic system is leading to when "undefined" and "philosophical fixes" are being subtly and insidiously (and I suspect totally unwittingly) INTRODUCED to the mathematics system in order to 'rescue' said axioms from incompleteness states/results . So whether that 'works' as presented, it does not address the very BASIS for that axiomatic treatment, does it? Hence the discussion/observations so far which you keep missing the intent of while you keep repeating 'textbook' counter-arguments which do not go to the actual points raised ABOUT the basis for what you repeat (which currently ultimately depends on circuitous self-serving and trivial 'proofs' which need the 'hidden' PHILOSOPHICAL 'fixes" currently INHERENT in the mathematics system to make them 'work' at all).

See? That's what I am trying to REMOVE from the current system, all those hidden philosophical 'external justifications' and 'fixes' and 'loopholes' and 'assumptive leaps' which effectively make the mathematics system a 'hybrid construct' of maths AND philosophy, and NOT 'pure maths' at all.

Mate, Thanks but no thanks. Your repetitions are (as you would put it ) "painfull to read again and again ad nauseam". See you round, Trippy.

PS: Please also read my post #275 re GOEDEL's INCOMPLETENESS Theorem, so that you don't miss that context to the discussioin as well because, as you say, you don't read others posts. Thanks.

 

[Trippy]

Hi Trippy.

I already replied to that and pointed out that the convention has nothing to do with the action of multiplication ITSELF. That is why I observed to Pete about which is the more FUNDAMENTAL aspect, the convention to move a decimal point to the right", OR to bring the actual " tens" effect of the zero in "10 x 0.9999. =9.9999..." expression? Convention is NOT action, just a formatting convenience, as you say. There is a difference between fundamental actions and conventional conveniences of formatting. Please ALL the relevant posts/exchanges on this aspect for the CONTEXT in which this observation was raised. Thanks.

I have read the exchanges, and it has not changed my opinion, you're still wrong. Good god man. Should I translate it into swahili for you? Would that help?

And I repeat to you - your argument is the convenience of formatting, not the other way around. Your argument leads to logical inconsistencies and nonsense statements which I have pointed out to you, and you have, once again, failed to address.

Mate, what can I say? Perhaps it would be best if we ended our exchange instead of continuing in the vein you seem to be (whether intentionally or unintentionally) taking it?

I'm not Australian, even if I was it would make no difference, I'm not your mate and I don't appreciate you addressing me with the term.

I mean, you seem emotional rather than disinterestedly objective.

Wrong - I'm not the one that spent 4 paragraphs because they took umbrage at a 16 word sentence.

You admit to being pained when reading others posts...

No, I said that your posts are at times painful to read. Do you understand the difference? You and I have had multiple exchanges over the course of time about what you could do to improve your posting style.

...and to not reading other background relevant exchanges in the thread which may inform you better as to the actual stage of the discourse and so prevent you making inadvertent strawmen and cross-purpose replies etc.

What I said was that I'm not in the habit of reading response to other peoples posts. If I never read responses to other peoples posts I'd never get involved in conversations would I? Your misrepresentation of my position is demonstrably false - the evidence is in the fact that I have participated in this conversation and in the post I made which preceeded this one.

Stop making assinine assumptions about what other people do or do not do.

Add to all that 'personal' attitude the further threat as a mod in order to intimidate and to take advantage of your mod position/power to make obviously personally disparaging 'framings' and 'glib dismissals' and 'characterizations' like "crank" and "word salad" etc etc.

Liar - I have not called you a crank (yet). Instead of complaining about the uses of phrases such as 'word salad' to describe your posts, or parts of your posts, perhaps you would be better off putting on your big boy pants, re-examining the portion of the post in question and considering how you could express the idea more clearly.

Now is that any way for a proper moderator on a good science site to behave nowadays?

Not your call. I've addressed the points you have raised, you seem instead focused on the smallest sleight. Put on your big boy pants, you're 64 ferchrissakes, act like it.

Ir is redolent of the past when trolls and compliant mods would collude for personal agendas to frame and ban people because they dared to question objectively and fairly discuss while being constantly baited and framed for banning by mods who behaved similarly (but worse then) to how you are behaving now.

More accusations. Wasting more time addressing a 16 word sentence. How many paragraphs are we at now?

You seem to be emotional and repetive in your glib 'proofs' which depend on similar glib assumptions all the way down the line irrespective which starting assumptions/expressions you have presented so far as 'counteragument' 'proof' examples.

Another paragraph complaining about the proofs rather than addressing them and actually contradicting them.

You obviously miss the context and the proper implications because you admit you don't read others and read them emotionally (pained) when you do.

Demonstrably a lie.

You are obviously incapable of treating the issues raised with fairness and without bringing threats and intimidation as mod in order to force YOUR personal and emotive opinions/prejudices 'baggage' etc on others unconvinced by your replies so far.

Another demonstrable lie.

It would be counter-productive to continue discussion here with you, Trippy, as you seem to be getting more personal, threatening and emotional as it goes on.

You're just looking for excuses to weasle out of addressing the pointgs that I have raised.

Therefore, mate, I humbly request you ignore my posts altogether and not respond in future, because your 'personal baggage' and 'emotionality' is neither good for objective discourse here nor good for your image/standing as mod here. Thanks anyway for your contribution/exchange so far, Trippy. Good luck in the future, and enjoy your objective science.maths discussions without all that emotion, mate. It's not good for the blood pressure! No hard feelings this end. See you round.

You're the only person bringing emotional baggage into this conversation. The only thing I have done is 1. Point out that at this time you're in contravention of the sites rules by posting as a sock puppet of a previously banned user. 2. Restate something which I have said to you half a dozen times across three seperate fora - that at times your posts are difficult, approaching physically painful to read because of your writing style.

The fact that I have not banned you when I have the power, and what I consider to be sufficient cause to do so is manifest proof that your complaints about personal bias or baggage on my part are bullshit. Take a moment to think about it RC, then try again.