# 1=0.999... infinities and box of chocolates..Phliosophy of Math...

rr6 said:
I dunno if geometry can be used to help clarify or resolve the connundrum?) crux of this infinite vs finite issue.
That you still think there is a conundrum means you really "dunno".

You've got a triangle with equal angles of 60[sup]o[/sup], a finite number. You appear to be unable to recognise that this is 1/3 x 180[sup]o[/sup], and 1/3 is 0.333... which is also a finite number. You also don't seem to be able to recognise that 1/3 is not irrational (if it was it would not be represented as the ratio of two finite numbers, namely 1 and 3).
And you don't seem to be able to recognise that 1/3 is not infinite.

I think your problem is that you just don't understand basic math. Did you finish grade school?

Wheres The Beef Arfa-Brane? Complex > Pahtway > Simple---NADA/Zero/ZIP

arfa brane--That you still think there is a conundrum means you really "dunno"."

I know that there is controversy-- that I'm specifically a part of ----regarding a crux/connundrum involving the issue of a finite 1.0 = infinite 0.999...

What your "dunno" is I dunno. It appears to me as troll-like uneccesary mental head-slap( digg ). Before I go into the below, if and when--- never is my best guess ---want to offer us( and I repeat ) a rational, logical, common sense and relatively simple explanatory guide for 99% of humanity to understand how/why a finite 1.0 = and infinite 0.999...., then please share.

I have not seen such by anyone, although appears to claim he gave us such. His set of two formula as a proof is laughable to me, as he gave little to no explanation, rather he just gives more typical troll-like head-slapping.

You've got a triangle with equal angles of 60[sup]o[/sup], a finite number. You appear to be unable to recognise that this is 1/3 x 180[sup]o[/sup], and

Huh? ABrane, first of all you appear to be attempting to say, that, somehow 0.3 or some rendition of that is equal to the number 60.

1) 0.3 * 180 = 54
...1a) 0.33333 * 180 = 59.9994

Without any explanation you want me to believe that, 0.333... does not represent and infinite value. Duhh, what/why do you think has been the crux/connundrum(?) of this topic/issue from its inception?

My understanding-- and I believe many others if not 99% of humanity placed in our circumstances ---will also believe, that 0.333... is representative of both an infinite value and irrational number. It is like a tag team wrestling with the opposing team on this issue i.e one person eventually posts to me and inference, that, 0.333... is not infinite, anpther that infers that, it is not irrrational, and another something else that I forget.

1) if 0.999...does is not representative of infinite value, then this topic/issue is not a crux/connundrum(?) from day one of its posting. I don't agree with that assessment, and

2) 0.999... and 0.333... appear to me to be irrational numbers or irrational decimals if that is more specific/precise. I dunno.

1/3 is 0.333... which is also a finite number. You also don't seem to be able to recognise that 1/3 is not irrational (if it was it would not be represented as the ratio of two finite numbers, namely 1 and 3)....
And you don't seem to be able to recognise that 1/3 is not infinite.

I think your playing mathematical head games with me ABrane, because no one-- except you a few posts back in this thread or the other one of similar topic ---has made this assertion to me as a statement of fact, rather they go giving all kinds of complex explanations never stating what your alledging here above. So there going on as if there is finite value vs infinite value crux/connundrum(?) when there perhaps never was.

What I understand, after doing Origins given formula on cal. is that, some numbers--- 9, 7, 6, 3 ---fill all of the available spaces on my MS cal. ergo I believe that infers/implies/suggests and infinite value. If that is incorrect, then your correct I do not understand the point of this finite 1.0 = infinite 0.999..., because you are inferring/implying.suggesting that 0.999...does not and is not an infinite value.

Duhh, I have been referencing 0.999.... as an infinite value all along, so as long as you can accept that as and fair representations--- as obvious many here and in the other thread have been doing ---then there is finite vs infinite crux/connundrum(?) and your above is attempt to throw my head into tail spin and keep you from giving us something you nor anyone else here has. A rational, logical, common sense and reltively simple explanatory guide as to how a finite 1.0 = infinite 0.999....

You appear to me, to want to change the rules of the game, midstream, because you cannot address my above, as stated and not just by quoting my comments and pretend that actually addresses them.

That said, I begin with 0.333..being representative of an infinite value. If you do not agree then we cannot have a rational conversation in regards to 0.333... * 180 = n

I think your problem is that you just don't understand basic math. Did you finish grade school?

That may be true to whatever degree, but if you want to play this mathematically intellectual game fairly, then we have to play by the same rules and not be chainging them midstream.

I have from very beginning laid out in earnestly and sincerely, the rules of the mathematically intellectual game I've been playing all along, based on what I believe to be the facts of this finite 1.0 = infinite 0.999... topic/issue;

1) 0.nnn...i.e. any number( n ) with the dots after word represent and infinite value,

2) 0.nnn.... i..e any number( n ) to right of decimal point is irrrational.

That I don't understand why the some numbers appear to me to give infinite values and others do not is perhaps a clue that I'm mispercieving something in all of this disscussion and apparrently other people becuase it appears to me, that, that finite vs infinite has been the point of crux/connundrum(?) all along.

This is reminiscent of the transcendental Pi, not technically being an infinite value, yet for most 995 of humanity, it does appear to function that way. Alpha-numeric made this point clear to me, although it is not really that clear, and he even help to validate the unclarity of why Pi is not technically an infinite value, when he stated that, Pi is a non-terminating decimal. Ha!

I asked him to direct me to thread that disscusses why/how a non-terminating decimal is not equal to infiinite value?

He did not direct me to any thread of such nature. So ABrane, in addition to my requests of you above, we can add to that list, direct me to thread that disscuss's how/why 0.999...and or 0.333.... or any number( n ) is not representative of;

1) 0.nnn... = infinite value,

2) 0.nnn... = irrational value.

Thx, and hope I covered all of your concerns.

R6

...well do the thought experiment yourself!
Reduce a ball so that it is the smallest it can be with out being zero.
and then ask yourself some questions about it's 3 dimensional vs zero dimensional reality

Then ask yourself : "Does currently held math use of a zero dimensional point still hold as totally valid?"

I think you are confusing or mixing up Math with Physics. Math is ideal, theoretical in its approach whereas Physics is more practical based on real evidence.

A dimension-less point is a mathematical concept and is the smallest. In Physics the smallest is the smallest particle or the Planck's Dimension.

Within this Planck's dimension(length), infinite mathematical points can be placed. So, in your thought experiment you can not reduce a ball beyond Planck's dimensions. Hence a ball can not be reduced to a mathematical point.

A mathematical point is dimensionless but it still exists and infinite number of such points make a finite dimension.- This is the beauty of Mathematics.

You also don't seem to be able to recognise that 1/3 is not irrational (if it was it would not be represented as the ratio of two finite numbers, namely 1 and 3).

Pi is the ratio of two finite numbers, namely pi/1. So pi is rational. I learn so much here.

someguy said:
Pi is the ratio of two finite numbers, namely pi/1. So pi is rational. I learn so much here.
Well, I should have said the ratio of two integers or natural numbers, but I didn't want to confuse the poor guy.

But pi is the ratio of a circle's circumference to its diameter, both finite numbers which are real. A bit of exploration shows that if the diameter is a whole number, then the circumference is not. That a rational number is the ratio of two finite numbers isn't false, but is a necessary condition, although not also a sufficient condition.
rr6 could of course have worked this out for himself (ha ha).

rr6 said:
I know that there is controversy-- that I'm specifically a part of ----regarding a crux/connundrum involving the issue of a finite 1.0 = infinite 0.999...
Again with the "infinite 0.999...". Where are you getting this from? 0.999... is not an infinite number.
Without any explanation you want me to believe that, 0.333... does not represent and infinite value.
0.333... = 1/3. 1/3 is not an infinite number. You can't see this?
1) 0.nnn...i.e. any number( n ) with the dots after word represent and infinite value,
No that's wrong. The "..." does not mean the number is infinite. How do you expect a rational discussion when you don't even understand the notation? This notation isn't advanced stuff, it's taught to grade schoolers.
Duhh, I have been referencing 0.999.... as an infinite value all along, so as long as you can accept that as and fair representations--- as obvious many here and in the other thread have been doing
If that's what you think, then you're blind as well. Nobody else thinks that 1/3 is an infinite number, your all on your own with that.

I think you are confusing or mixing up Math with Physics. Math is ideal, theoretical in its approach whereas Physics is more practical based on real evidence.

A dimension-less point is a mathematical concept and is the smallest. In Physics the smallest is the smallest particle or the Planck's Dimension.

Within this Planck's dimension(length), infinite mathematical points can be placed. So, in your thought experiment you can not reduce a ball beyond Planck's dimensions. Hence a ball can not be reduced to a mathematical point.

A mathematical point is dimensionless but it still exists and infinite number of such points make a finite dimension.- This is the beauty of Mathematics.

Ahh.... but the beauty of a thought experiment is that it is not limited by the rules of a system in place at the time. It merely poses a question as it stands regardless of whether another abstraction can impose some sort of inhibition.
The experiment regardless of the scientific system required is simply:

Reduce a ball to the smallest it can be but remain greater than zero...
Assess you observations using what ever tools you have.
Question: Can a Planck dimension be divided in half?
What exists if it is less than a Planck dimension?

I think you are confusing or mixing up Math with Physics. Math is ideal, theoretical in its approach whereas Physics is more practical based on real evidence.
Perhaps you fail to see the significance... [not unexpected as it isn't easy to see]

If you note any given volume of space and perform this thought experiment at any location you will came to realize that both the zero dimension and 3 dimensions co-exist simultaneously. That the distance between say the Earth and the Moon is both a real 3 dimensional metric and zero simultaneously. In fact it could be seriously considered that the entire universe is both three and zero dimensional simultaneously.
Suddenly you have a potential vehicle for the understanding of inertia, and the universal constancy of gravity...

Especially when you consider that when undergoing cosmic metric expansion zero remains the only universal constant, it all tends to become more useful.
Extended example:
The permeability and permittivity of space could be directly related to the tension that may exists between 3 dimensions and zero dimensions co-existing universally. Thus invariance is possible in an expanding or contracting or stable universe.

Arfa Brane Cannot Address Finite 1.0 = Infinite 0.999...Crux/Connundrum As Stated

Again with the "infinite 0.999...". Where are you getting this from? 0.999... is not an infinite number. 0.333... = 1/3. 1/3 is not an infinite number. You can't see this? No that's wrong. The "..." does not mean the number is infinite. How do you expect a rational discussion when you don't even understand the notation? This notation isn't advanced stuff, it's taught to grade schoolers.If that's what you think, then you're blind as well. Nobody else thinks that 1/3 is an infinite number, your all on your own with that.

infinite 0.999... is an infinite value is what I have believed all along and that has been the languge I have been using all along as the basis of my crux/conundrum regarding finite value vs infinite. I have been very clear on this point, repeately.

0.9 is not the same as infinite 0.999... i.e the dots afterword actually mean infinite( to me ) and many others on planet Earth and if you need a two little circles in a figure 8( oo ) instead, then put those in there. You seem to be an intellectual sort, you should be able to concept/mentally replace the dots with oo to feed your need to connect my words 'infinite' to some kind of a texticonic symbol. Childs play so you should be able handle it. I dunno.

My message/content amounts to same thing either way, and you nor anyone else can give a rational, logical, common sense and relatively simple, explanatory guide of a proof that equates finite 1.0 to infinite 0.999...oo...oo...oo....

There I gave you extra dots texticonic infinite symbols to feed your need for something other than or in addition to dots to connect the word 'infinite' to my given number. Duhh, it is childs play dude and you want to play nit-picky games, because you have not and cannot, give us a rational, logical, common sense and relatively simple, explanatory guide of a proof that equates finite 1.0 to infinite 0.999...oo...oo...oo....

As always I' not going to wait for to address my comments specifically as stated and just quote them as tho that alone means something.

Pi is transcendental, however, it behaves similarly, to some numbers, when they are divided by 9, 7, 6 and 3 i.e. the fill all of the spaces on the calculator, whereas 8, 5, 4 adn 2 do not fill all the spaces of the cal.

I told you this before and you do not address that adn to me that is a sign of going infinite-- or 'going mental'( saturday night live ) --- i.e. if the the spaces of the cal. were infinite then the cal, would never stop processing when we type Pi, or when divide some numbers by 9, 7, 6, and 3.

I repeat, Alpha made it clear to me, that, Pi is not an infinite number, yet does appear to function that way, in some if not circumstances.

That is an aside tho, and you and others need to meet the other criteria I have challenged you to do and have not, cannot, will not ever do. Why?

Because a finite value can never be equal to an infinite value except maybe through some very comlicated matematically illusionary, mental masturbation associated with "mapping" and using words like subjerctive and injerctive etc.....oops there are those dots again.

Could "etc..." be associated with a non-terminating set of concepts? Ha ha!

I think there are bunch of people here who have a large ego block to truth of this topic of finite 1.0 NOT equal to infinite 0.999...

r6

Hi rpenner.

Not possible in axiom systems where length is parametrized by the rational numbers, the real numbers, the hyperreal numbers or the surreal numbers for if x is claimed to be the smallest positive number, x/2 must be a legal number, positive and smaller yet.

From what I can observe of your x/2 line of reasoning, the axiom assumes that 'something' ('number') can be REPEATEDLY sub-divided into equal 'smaller and smaller' parts without limit. Is that what you wish to imply by that line of reasoning/axiom you use there?

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rr6 said:
infinite 0.999... is an infinite value is what I have believed all along
And you continue to believe it.

That's because you don't understand that the "..." means you repeat the digits infinitely. You're saying you don't know the difference between an infinitely repeating decimal and an infinite number. The infinite number is the number of decimal places, and you haven't picked that up in this thread because you don't want it (the bleedingly obvious) to change your mind.

Because you're a muppet.

Sorry Arfa Brane Still No Banana For Lack of Addressing Core Issue

And you continue to believe it.That's because you don't understand that the "..." means you repeat the digits infinitely. You're saying you don't know the difference between an infinitely repeating decimal and an infinite number. The infinite number is the number of decimal places, and you haven't picked that up in this thread because you don't want it (the bleedingly obvious) to change your mind.
Because you're a muppet.

Huh? Now your saying the "..." do equal infinite. Dude you need to get your head on straight.

Have the dots mean anything you want them to, if it feeds your mental cookie. Didn't I tell you to replace or add a infinity sign( oo ) to help feed your mental ability to grasp when I say infinite I mean infinite 0.999...irrespective what texticons your mentality has to have to feed its cookie.

Once again, you have no rational, logical, common sense and relatively simple explanatory guide to understanding your and or others claims, that finite 1.0 = infinite 0.999.... Nada/Zip/Zero on your part because your incorrect and your ego can't handle it.

finite value equaling an infinite value is mathematically illusionary, mental masturbation. End of story.

Come back and talk to me when you want to address the specifics of my comments as stated and not your nit picky details that are all and aside to fact of the matter, and that is finite value of 1.0 NOT equal to infinite value of 0.999.....

Once again, maybe you need to read Origins simple two lines of formula as a proof of finite 1.0 = infinite 0.999...and then maybe you can begin to have a basis for believing such and illogical, irrational, far from common sense idea, and begin to offer us a rational, logical, common sense and relatively simple explanatory guide. Ha! NOT.

So sorry Arfa, no banana for you yet, at least on the primary topic, and as always, i will not be holding my breath for you to address my comments specifically as stated, and not just quoted for convenice sake.

Lets see now, who was that wants to keep changing the rules of the game midstream? It wont be long and these dudes will start changing the rules again and state they never stated, infered/implied that finite value of 1.0 = infinite value of 0.999.....

Believe me, some if not all of those on the other side have little to no moral and intellectual integrity in regards this issue. I agree that it is not a connundrum/crux, becuase they are just plain incorrect and no amount of veruy complex, mathematically illusionary, mental masturbation is ever going to prove there side, much less a very simple--- see Origin for NO explanation ---explanation.

Here again, I can do a simple "mapping" illusion. I say that finite value 1.0 = A in column FF and then I move it too column ZZ and I rename it T and T is equal to the infinite value 0.999....

So there, I did simple "mapping". Not complex. Hey Origin, want to borrow my simple explanation?

r6

rr6 said:
Huh? Now your saying the "..." do equal infinite. Dude you need to get your head on straight.
Dude, you need to take remedial reading lessons.

Still don't get the difference between an infinite-valued number and an infinite number of decimal places which represents a finite-valued number? That's too bad.
Have the dots mean anything you want them to, if it feeds your mental cookie.
Well obviously they don't mean much to you, and nor does mathematics. Who do you think cares?
Probably not Ronald McDonald, but I doubt he would let you get near a till.

Arfa Seeing Infinite Set of Dots...oo..Spaces..oo...Dots...oo...Spaces.....

Dude, you need to take remedial reading lessons. Still don't get the difference between an infinite-valued number and an infinite number of decimal places which represents a finite-valued number? That's too bad.Well obviously they don't mean much to you, and nor does mathematics. Who do you think cares? Probably not Ronald McDonald, but I doubt he would let you get near a till.

You dont care about offering us a rational, logical, common sense and relatively simple explanatory guide for a finite value 1.0 = infinite value 0.999... because the do NOT equal. Why? Because you nor anyone can. Is that an infinite truth?

You need to get Origin to help you at least get a couple of simple formula together, and then maybe you can work from that. He states

1/3 = 0.33333333333333333333333333333333......... oops,sorry Arfa, those dots were not on my cal., ergo, your correct I have no idea if this is an infinite value or and infinite number value with infinite dots aftewords ergo an infinite connundrum/crux(?).

infinite 0.999... is NOT equal to finite 1.0.....imho

3.1415926535897932384626433832795.... = "non-terminating decimal" if I recall Alpha correctly. Please direct me to the thread that debates the differrence between "non-terminating decimal" and infinite decimal. Yeah, just as I thought you can't do that either because no such thread exists here at Sci-F.

1) infinite value,

2) infinite value number,

3) infinite number of decimal places,

4) "non-terminating decimal",

5) macro-infinite spaces or space

6) micro-infinite spacees or space

7) infinite set,

8) oo..oo..oo..oo..oo..???....Ronald Mc Donald????...oo...

What is Ronald Mc Donald doing out there in infinite space(s)?????....

Axioms are needed before a thought experiment is more than mental masturbation.
This is expressing that unless you clearly assert what your principle assumptions are and develop those assumptions using logic and clear language, there is no possible meeting of the minds.
Reduce a ball so that it is the smallest it can be with out being zero.

Not possible in axiom systems where length is parametrized by the rational numbers, the real numbers, the hyperreal numbers or the surreal numbers for if x is claimed to be the smallest positive number, x/2 must be a legal number, positive and smaller yet.

From what I can observe of your x/2 line of reasoning, the axiom assumes that 'something' ('number') can be REPEATEDLY sub-divided into equal 'smaller and smaller' parts without limit. Is that what you wish to imply by that line of reasoning/axiom you use there?
That's one way of putting it. But a better way of putting it is for the rational numbers or the algebraic numbers or the real numbers or the complex numbers, there is always a distinct third number halfway between any two distinct numbers. (The integers don't have this property, obviously.)
This property of the real numbers has a geometric analogy in Euclid's Elements of Geometry, Book I, Postulate 1 and Proposition 10.
And you see the simple idea formally developed from the axioms of real numbers and set theory:

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Ahh.... but the beauty of a thought experiment is that it is not limited by the rules of a system in place at the time. It merely poses a question as it stands regardless of whether another abstraction can impose some sort of inhibition.
The experiment regardless of the scientific system required is simply:

Reduce a ball to the smallest it can be but remain greater than zero...
Assess you observations using what ever tools you have.
Question: Can a Planck dimension be divided in half?

In Physics, Planck's dimension can not be divided. In mathematics you can.
What exists if it is less than a Planck dimension?

This thought experiment can only be done in mathematics.

Perhaps you fail to see the significance... [not unexpected as it isn't easy to see]

Your thought experiment is not possible in Physics.

If you note any given volume of space and perform this thought experiment at any location you will came to realize that both the zero dimension and 3 dimensions co-exist simultaneously. That the distance between say the Earth and the Moon is both a real 3 dimensional metric and zero simultaneously. In fact it could be seriously considered that the entire universe is both three and zero dimensional simultaneously.

how?
Suddenly you have a potential vehicle for the understanding of inertia, and the universal constancy of gravity...

What is potential vehicle?

Especially when you consider that when undergoing cosmic metric expansion zero remains the only universal constant, it all tends to become more useful.
Extended example:

How?

The permeability and permittivity of space could be directly related to the tension that may exists between 3 dimensions and zero dimensions co-existing universally. Thus invariance is possible in an expanding or contracting or stable universe.

How?

Your thought experiment is not possible in Physics.
how?
What is potential vehicle?
How?
How?
If the thought experiment is not possible to be done in physics then I guess there is no point discussing it...

"..." Represent Infinite Pprocess/Procedure

"..." dots represent infinite value and a infinite process/procedure and no amount of mind playing games with grammar or mathematics is will change that, in regards to 1.0 NOT equal to 0.999....

Those in the camp of 1.0 = 0.999... are playing mathematically illusionary, mental masturbation games. imho

This is simple conclusion and does require complex "mapping" math to understand but rather only rational, logical and common sense to understand.

To have 1.0 = 0.999... there are two simple processes that have to happen;

1) STOP the infinite process i.e. remove and exclude the dots from the value, number, equations( wiki ) whatever,

2) then round 0.9 higher to 1.0.

This is rational, logical common sense and certainly a relatively simple explanatory guide to understanding that 1.0 does NOT equal 0.999....

No amount-- thousand of years --- of flawed thought process and flawed/invalid mathematics will ever make a false irrational nonsense a rational common sense fact/truth. imho

r6

Those in the camp of 1.0 = 0.999... are playing mathematically illusionary, mental masturbation games. imho
Except since the question is about the value of 0.999... as a real number, just like saying π = 3.14159... is a statement about a real number and a representation with an infinite number of digits, then the proper domain is the field of real analysis which requires knowing what the rule of the game are.

You are perfectly free to ignore the real numbers, but then you lose any credibility you have on the topic of mathematics until you pick a set of rules and stick to them. So far rr6, your use of imperfectly understood Windows calculator tools instead of mathematics is not serving you well.