That's already been done - the proof is simple. Use a calculator, or do the long division.
1 is 0.9999999999999............
- Thread starter chinglu
- Start date
That's already been done - the proof is simple. Use a calculator, or do the long division.
The division algorithm is recursive. That means it can only achieve a finite number of digits.
So, how exactly are you making a computer program achieve anything other than a finite number of digits even if it never halts?
Just a naive note that may be of use:
when calculating an equation, are we assuming it to take time to do so... ie.
is 1+1=2 and instantaneous sum or is it a time sequential sum.
The reason I bring this up is that as with the calculating of Pi to 2 billion digits.... simply stating Pi in an instant of time is sufficient.
So when saying 9.999... we are at that point stating the entire number and no time to calculate is involved.
The problem with working with infinities is that we tend to conceptualize the calculation as being a... calculation...(steps==>conclusion.)/t
When dealing with infinities this may have a significant bearing on how the result is seen...thus conceptualized.
just thoughts...
Hi rpenner. 
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...
Precisely. The context is what affects the treatment of zeros, as I have been saying. See my previous posts and especially my last to Trippy regarding this particular aspect regarding which 'contextual' treatment/action is the more fundamental and less trivial when compared to other less fundamental and more trivial (self-serving definitions/choices) effectively inherent to the current incomplete mathematics system treatments/conventions invoked in 'proofs' based on same incomplete 'starting assumptions' etc. Thanks.
Oh, just to be clear where this is coming from, I am assuming you DO agree that the current status quo of the mathematics system/construct IS incomplete? Yes? Which is why my 'from scratch' approach to bring it all back to the most fundamental stages BEFORE the 'incompleteness trail' sets in irretrievably?
Again, please also read my previous posts to Trippy et al, especially my last to Trippy; as it will help clarify where I am coming from on all this. Thanks.
I also noted this particularly...
And right there you are depending on 'inescapable' rules of an incomplete mathematics. How 'sound' is that when discussing the axioms and rules themselves anew to examine their potential for leading to "undefined" and other 'self-referencing 'trivial' proofs depending on such EXTERNAL add-ons as INFINITY and other philosophical NON-sequitur 'justifications for the 'rules' and treatments'?
If it is agreed by all here that INFINITY is a CONCEPT and NOT a NUMBER, then the current mathematics 'rules' and 'definitions' and 'proofs' (especially LIMITS arguments based on a concept rather than ONLY ON THE NUMBERS consistent with the rules BEFORE these 'loophole' add-ons are introduced) in order to make the INCOMPLETE maths appear to be consistent, but which in fact is IN-consistent because it ultimately relies on EXTERNAL introductions of CONCEPTS from OUTSIDE the mathematics construct itself. Only by such trivial/arbitrary extensions into philosophical concepts such as "infinity" and "undefined" states can the current incomplete mathematics be made to 'look like' but isn't consistent from the actual axioms without any philosophical add-ons and loopholes (like the Limits and Infinity etc EXTERNAL CONCEPTS which do not really exist in any way that can be used AS part of a purely NUMBER system and the mathematics which supposedly follows from axioms based on such number systems WITHOUT the arbitrary philosophical "loopholes" and "proofs" and other non-fundamental trivialities and treatments 'contrived' therefrom).
Again, please read my earlier posts to Pete, Trippy et al for further clarification where I am coming from in context in this particular discussion and points raised. If word salad is what you 'read' it as, then try just looking beyond personal kneejerking and unintentional strawmanning approaches to reading others fairly on what is presented in this Alternative Theories section discussion, preferably without reference to the person's status/history or anything irrelevant to the points at all. Thanks, rpenner, Trippy, Pete, QQ and everyone!
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...
Precisely. The context is what affects the treatment of zeros, as I have been saying. See my previous posts and especially my last to Trippy regarding this particular aspect regarding which 'contextual' treatment/action is the more fundamental and less trivial when compared to other less fundamental and more trivial (self-serving definitions/choices) effectively inherent to the current incomplete mathematics system treatments/conventions invoked in 'proofs' based on same incomplete 'starting assumptions' etc. Thanks.
Oh, just to be clear where this is coming from, I am assuming you DO agree that the current status quo of the mathematics system/construct IS incomplete? Yes? Which is why my 'from scratch' approach to bring it all back to the most fundamental stages BEFORE the 'incompleteness trail' sets in irretrievably?
Again, please also read my previous posts to Trippy et al, especially my last to Trippy; as it will help clarify where I am coming from on all this. Thanks.
I also noted this particularly...
And right there you are depending on 'inescapable' rules of an incomplete mathematics. How 'sound' is that when discussing the axioms and rules themselves anew to examine their potential for leading to "undefined" and other 'self-referencing 'trivial' proofs depending on such EXTERNAL add-ons as INFINITY and other philosophical NON-sequitur 'justifications for the 'rules' and treatments'?
If it is agreed by all here that INFINITY is a CONCEPT and NOT a NUMBER, then the current mathematics 'rules' and 'definitions' and 'proofs' (especially LIMITS arguments based on a concept rather than ONLY ON THE NUMBERS consistent with the rules BEFORE these 'loophole' add-ons are introduced) in order to make the INCOMPLETE maths appear to be consistent, but which in fact is IN-consistent because it ultimately relies on EXTERNAL introductions of CONCEPTS from OUTSIDE the mathematics construct itself. Only by such trivial/arbitrary extensions into philosophical concepts such as "infinity" and "undefined" states can the current incomplete mathematics be made to 'look like' but isn't consistent from the actual axioms without any philosophical add-ons and loopholes (like the Limits and Infinity etc EXTERNAL CONCEPTS which do not really exist in any way that can be used AS part of a purely NUMBER system and the mathematics which supposedly follows from axioms based on such number systems WITHOUT the arbitrary philosophical "loopholes" and "proofs" and other non-fundamental trivialities and treatments 'contrived' therefrom).
Again, please read my earlier posts to Pete, Trippy et al for further clarification where I am coming from in context in this particular discussion and points raised. If word salad is what you 'read' it as, then try just looking beyond personal kneejerking and unintentional strawmanning approaches to reading others fairly on what is presented in this Alternative Theories section discussion, preferably without reference to the person's status/history or anything irrelevant to the points at all. Thanks, rpenner, Trippy, Pete, QQ and everyone!
Nope, this is not it.
You cannot produce anything other than a finite sequence finite from recursion.
If you can, prove your case. I already proved it cannot be done.
Hi rpenner.
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...
Precisely. The context is what affects the treatment of zeros, as I have been saying. See my previous posts and especially my last to Trippy regarding this particular aspect regarding which 'contextual' treatment/action is the more fundamental and less trivial when compared to other less fundamental and more trivial (self-serving definitions/choices) effectively inherent to the current incomplete mathematics system treatments/conventions invoked in 'proofs' based on same incomplete 'starting assumptions' etc. Thanks.
Oh, just to be clear where this is coming from, I am assuming you DO agree that the current status quo of the mathematics system/construct IS incomplete? Yes? Which is why my 'from scratch' approach to bring it all back to the most fundamental stages BEFORE the 'incompleteness trail' sets in irretrievably?
Again, please also read my previous posts to Trippy et al, especially my last to Trippy; as it will help clarify where I am coming from on all this. Thanks.
I also noted this particularly...
And right there you are depending on 'inescapable' rules of an incomplete mathematics. How 'sound' is that when discussing the axioms and rules themselves anew to examine their potential for leading to "undefined" and other 'self-referencing 'trivial' proofs depending on such EXTERNAL add-ons as INFINITY and other philosophical NON-sequitur 'justifications for the 'rules' and treatments'?
If it is agreed by all here that INFINITY is a CONCEPT and NOT a NUMBER, then the current mathematics 'rules' and 'definitions' and 'proofs' (especially LIMITS arguments based on a concept rather than ONLY ON THE NUMBERS consistent with the rules BEFORE these 'loophole' add-ons are introduced) in order to make the INCOMPLETE maths appear to be consistent, but which in fact is IN-consistent because it ultimately relies on EXTERNAL introductions of CONCEPTS from OUTSIDE the mathematics construct itself. Only by such trivial/arbitrary extensions into philosophical concepts such as "infinity" and "undefined" states can the current incomplete mathematics be made to 'look like' but isn't consistent from the actual axioms without any philosophical add-ons and loopholes (like the Limits and Infinity etc which does not really exist in any way that can be used AS part of a pure;y NUMBER system and the mathematics which follows from axioms based on such number systems WITHOUT the arbitrary philosophical "loopholes" and "proofs" and other non-fundamental trivialities and treatments 'contrived' therefrom.
Again, please read my earlier posts to Pete, Trippy et al for further clarification where I am coming from in context in this particular discussion and points raised. If word salad is what you 'read' it as, then try just looking beyond personal kneejerking and unintentional strawmanning approaches to reading others fairly on what is presented in this Alternative Theories section discussion, preferably without reference to the person's status/history or anything irrelevant to the points at all. Thanks, rpenner, Trippy, Pete, QQ and everyone!
rpenner, Trippy, Pete, QQ have not produced any sound mathematical proofs to support their cases.
If they have, then show it here by induction.
Gosh! You are trying to fit way too much into a single sentence Undefined...
You really do need to take smaller steps in your dialogue... IMO
The greatest complaint you will find against this approach of yours, is that to argue the case against something, you need to know that something first. You not only need to know it, you need to prove that you know it in a way that is "masterful" and that is why changes to mathematical systems, I would imagine are incredibly rigorous and "life time" consuming.
In this example of the way infinity is being used by THIS number system [ Not Hyperreals or other but this particular number system] has been clearly explained by Tach and probably by Rpenner, however to fully appreciate that explanation you need to have a whole swag of other aspects of that number system under your belt.
Of course all number systems are far from perfect, Tach and Rpenner would be the first to admit this, but to offer a alternative requires a thorough understanding of what you are seeking to change as a primary objective and then take into account the "human" nature of the people who work to support that imperfect system. No easy task...
Easy, I already showed you this at the beginning of the thread but you didn't get it $$S_n=\frac{9}{10}+...+\frac{9}{10^n}$$
So, $$S_n=1-\frac{1}{10^n}$$
$$0<S_n<1$$ and $$S_{n+1}>S_n$$, the series is bounded and it is monotonic, therefore the series is convergent.
The limit is 1. Done.
Nah, I just point out your mistakes.
Hi QQ.
Well, briefly as I can while still explaining in 'word salad' my own 'take' on that question, IN MY OPINION, and according to my observations and the discussions/arguments so far, it appears to depend on which way one comes to that question.
If one comes to it from the direction of just being a definitional convention of notation to express some information about the 'background' to the expression BEFORE it was 'defined" to the bland "1", then there is NO real action involved in its 'presentation', and hence is not any kind of real action except an arbitrary convention application.
However, if one comes to it from the direction that it is the 'output' of a real action/operation, then one is constrained to explain the 'action background' consistent with the numbers having been 'arrived at' AS a number rather than just having been 'defined into existence' AS an expression substituting FOR "1" etc etc by definition and for no other real number action 'reason'.
Well, briefly as I can while still explaining in 'word salad' my own 'take' on that question, IN MY OPINION, and according to my observations and the discussions/arguments so far, it appears to depend on which way one comes to that question.
If one comes to it from the direction of just being a definitional convention of notation to express some information about the 'background' to the expression BEFORE it was 'defined" to the bland "1", then there is NO real action involved in its 'presentation', and hence is not any kind of real action except an arbitrary convention application.
However, if one comes to it from the direction that it is the 'output' of a real action/operation, then one is constrained to explain the 'action background' consistent with the numbers having been 'arrived at' AS a number rather than just having been 'defined into existence' AS an expression substituting FOR "1" etc etc by definition and for no other real number action 'reason'.
@chinglu
Can you explain in plain language what you mean by "finite sequence finite from recursion" [ not for me but for your critics?]
Been there, done that long ago, mate. I am 64 this month, and a strictly independent objective atheist and scientist since age 9; so I have forgotten (purposely in many case in order to 'start from scratch' without undue 'pre-conditioning' by 'training' rather than 'exploration anew' on my own) more real relevant stuff than most people have yet to encounter and comprehend. I am not sure who said this before in the science literature, paraphrased: "Sometimes it is necessary to 'unlearn' in order to review that learning and more from scratch to catch what may have been (almost inevitably) missed by the former status quo."
Anyhow, as I have tried to explain 'where I am coming from', when those very uses of Limits and Infinity etc etc imply the mathematics would fail unless such philosophical add-on "loopholes" are arbitrarily introduced and then used for 'proofs', it behoves one to step back from the current construct altogether to tease out what is or is not consistent with a purely number system sans philosophical overlay in order to make the rules which will naturally 'confirm' what the arbitrary philosophical overlay was introduced FOR precisely because the math system IS incomplete.
Being "masterful" in an incomplete maths system DEPENDENT obviously on "LOOPHOLES" enacted in order to PRETEND it is complete and therefore subject to "masterful" understanding of what is incomplete is no ay to adjure what one can or cannot do when reviewing the starting/fundamental assumptions/entities. Once one has understood that the incompleteness arises unless "infinity" and "undefined" philosophical stances are used as "loopholes", then one can move immediately back to the 'from scratch' default position because any "masterfuL understanding of the incomplete system and trivial/loophole-riddled 'proofs' for same is not very helpful but a hinderance if one is expected to cow-tow to a constraint FROM an incomplete system before one is 'allowed' to 'review' that system precisely because it is NOT "masterful" comprehension of something complete per se.
Yeah, sorry, QQ, about my long sentences, but that is what it is. If I try to be more stingy then the usual 'cross-purpose' misunderstandings come in and an endless request for further info. Better to short cut all that wasted trivial process and just include as much context and alternatives as possible as soon as possible. Of course it requires proper attention and reading patience/fairness. But that is what this site expects from genuine discoursers who aren't just interested in the 'soundbite' approach to scientific exchange without any personal stuff and distractions brought in by non-genuine readers or trolls.
Hi QQ.
Well, briefly as I can while still explaining in 'word salad' my own 'take' on that question, IN MY OPINION, and according to my observations and the discussions/arguments so far, it appears to depend on which way one comes to that question.
If one comes to it from the direction of just being a definitional convention of notation to express some information about the 'background' to the expression BEFORE it was 'defined" to the bland "1", then there is NO real action involved in its 'presentation', and hence is not any kind of real action except an arbitrary convention application.
However, if one comes to it from the direction that it is the 'output' of a real action/operation, then one is constrained to explain the 'action background' consistent with the numbers having been 'arrived at' AS a number rather than just having been 'defined into existence' AS an expression substituting FOR "1" etc etc by definition and for no other real number action 'reason'.
So basically you are rejecting what you perceive as a "Call to Authority"? yes...
wow!. long sentences are much worse than short succinct bullet points! The reading audience has an attention span of about 10 words I think they reckon...any thing longer and they tend to fall asleep at the wheel.Been there, done that long ago, mate. I am 64 this month, and a strictly independent objective atheist and scientist since age 9; so I have forgotten (purposely in many case in order to 'start from scratch' without undue 'pre-conditioning' by 'training' rather than 'exploration anew' on my own) more real relevant stuff than most people have yet to encounter and comprehend. I am not sure who said this before in the science literature, paraphrased: "Sometimes it is necessary to 'unlearn' in order to review that learning and more from scratch to catch what may have been (almost inevitably) missed by the former status quo."
Anyhow, as I have tried to explain 'where I am coming from', when those very uses of Limits and Infinity etc etc imply the mathematics would fil unless such philosophical add-on "loopholes" are arbitrarily introduced and then used for 'proofs', it behoves one to step back from the current construct altogether to tease out what is or is not consistent with a purely number system sans philosophical overlay in order to make the rules which will naturally 'confirm' what the arbitrary philosophical overlay was introduced FOR precisely because the math system IS incomplete.
Being "masterful" in an incomplete maths system DEPENDENT obviously on "LOOPHOLES" enacted in order to PRETEND it is complete and therefore subject to "masterful" understanding of what is incomplete is no ay to adjure what one can or cannot do when reviewing the starting/fundamental assumptions/entities. Once one has understood that the incompleteness arises unless "infinity" and "undefined" philosophical stances are used as "loopholes", then one can move immediately back to the 'from scratch' default position because any "masterfuL understanding of the incomplete system and trivial/loophole-riddled 'proofs' for same is not very helpful but a hinderance if one is expected to cow-tow to a constraint FROM an incomplete system before one is 'allowed' to 'review' that system precisely because it is NOT "masterful" comprehension of something complete per se.
Yeah, sorry, QQ, about my long sentences, but that is what it is. If I try to be more stingy then the usual 'cross-purpose' misunderstandings come in and an endless request for further info. Better to short cut all that wasted trivial process and just include as much context and alternatives as possible as soon as possible. Of course it requires proper attention and reading patience/fairness. But that is what this site expects from genuine discoursers who aren't just interested in the 'soundbite' approach to scientific exchange without any personal stuff and distractions brought in by non-genuine readers or trolls.
Not many people can remember the context of your sentence as it proceeds to your end point. ( 17 words - are you still awake! ?
)Any ways
IMO you are courageously attempting to merge philosophy with mathematics and from what I understand this is a labyrinth in a can of worms.
Until the "logic/rational/ reasoning/methodology" is sorted out in philosophical terms mathematics will automatically reject it. IMO
Example:
Philosophically infinite strings of decimal places can not ever achieve zero.... in some camps, in others it can.
Philosophically 1/infinity can only equal 1/infinity, certainly not zero... in some camps but not in others.
And it is being pointed out to you that you are only trolling and making noise. Just because you 'believe' that you are 'correcting' others, it doesn't change the fact that others have corrected YOU. And that many of your 'corrections' were WRONG in the context. And that you have been banned for just such 'noise' and baiting/distraction posts totally removed from proper on-topic discussions as per site rules. Please stop your spurious 'correction' claims and premature ejaculations of 'victory' and perpetual empty 'noise' while the conversation is still ON-GOING, Tach. Thanks for your future co-operation with the rules of the site, Tach.
I merely put the observations and arguments highlighting that being "masterful" on some incomplete and "infinity/undefined" riddled system is no basis for argument FOR that system from WITHIN that same incomplete and now-under-question system. If you interpret that succinctly as "rejecting what I perceive as a "call to Authority", then I will not disabuse you of that interpretation, but will ask all concerned to have regard the basis (as argued in my post) from which that perceived rejection arises.
Can I ask? Were you a lawyer or solicitor in your working life? [ don't answer btw the question is only a joke]I merely put the observations and arguments highlighting that being "masterful" on some incomplete and "infinity/undefined" riddled system is no basis for argument FOR that system from WITHIN that same incomplete and now-under-question system. If you interpret that succinctly as "rejecting what I perceive as a "call to Authority", then I will not disabuse you of that interpretation, but will ask all concerned to have regard the basis (as argued in my post) from which that perceived rejection arises.
Possibly legal reform would be more up your alley?
I bolded that last sentence.
Consider: I have just explained that it is the current mathematics which has introduced/mixed arbitrarily the PHILOSOPHICAL concepts:
- Infinity is not a "number";
- Limits tactics/treatments based on such philosophical concepts are essentially add-ons to the mathematics to use philosophy to 'paper over the gap' in the axiomatic number system/treatment and 'proofs'; and
- "undefined" is basically a 'get-out loophole' avoidance 'state' of "understanding masterfulness" to again avoid addressing that particular non-sequitur (arising from the number system axioms).
See? It is not I who am 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.
Was that clear and concise enough, mate?
@ undefined
as an aside,
Have you ever heard of a system that could be described as "Spherical, 3 dimensional reflective mathematics"? [ where the sum of the equations are in the center of a spherical layout and not at the ends in a Linea 2 dimensional format ]
as an aside,
Have you ever heard of a system that could be described as "Spherical, 3 dimensional reflective mathematics"? [ where the sum of the equations are in the center of a spherical layout and not at the ends in a Linea 2 dimensional format ]
gotta love those bullet points...I bolded that last sentence.
Consider: I have just explained that it is the current mathematics which has introduced/mixed arbitrarily the PHILOSOPHICAL concepts:
- Infinity is not a "number";
- Limits tactics/treatments based on such philosophical concepts are essentially add-ons to the mathematics to use philosophy to 'paper over the gap' in the axiomatic number system/treatment and 'proofs'; and
- "undefined" is basically a 'get-out loophole' avoidance 'state' of "understanding masterfulness" to again avoid addressing that particular non-sequitur arising from the number system axioms).
See? It is not I who am 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.
Was that clear and concise enough, mate?
sure is ...clear as a bell..
so what now...?
What do you have to learn and do to achieve your objective...?