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

Tach said:
But this is not what you write, you write the nonsense:

arfa brane
We just write numbers like 0.009 as 0.9, because it's: "0.009 multplied by 100".
How can a sane person write 0.009 as 0.9? They are two DIFFERENT numbers.
But that is not what I posted, it's an edited version. Edited by you to support your insanity.

You must be insane because you can't see that the zero of a repeating decimal is the same as a string of infinite zeros (my point, the same point as others such as Trippy have made, and one you eventually agreed is trivially true) but the zeros that extend to the right after division are not an infinite string.

You refuse to accept that I was referring to this zero, and how it must extend to the left, since 0.999... = 00.999... = (any number of leading zeros up to infinity).999... and keep beating the already dead and buried horse.

You like to see mistakes that aren't there because you're insane.

It's not my convention, it's the convention being taught at tertiary institutions around the world, it's for the same reason that 52,000 is two significant figures, not five.

Good for you.

My point being that, as I first stated twenty or thirty posts ago that there is an undending string of leading zeroes that we agree not to write unless we absolutely have to

True, but this is not what is being debated.

- for example, they're moved to the right of the decimal point, and there is another unending string of trailing zeroes after the last significant figure,

True, but this is not what is being debated.

and the insertion or deletion of zeroes when multiplying by powers of ten is simply as a result of performing operations on the decimal powers of the significant figures. It has nothing to do with moving the decimal point or adding zeroes to the end of the string.

Also true but this is not the subject of the debate. Do you know what the subject is?

You must be insane because you can't see that the zero of a repeating decimal is the same as a string of infinite zeros (my point, the same point as others such as Trippy have made, and one you eventually agreed is trivially true) but the zeros that extend to the right after division are not an infinite string.
For the sake of clarity - are you referring here to the string of zeroes between the decimal place and the first significant digit? Or the string of zeroes after the last significant digit?

Trippy said:
For the sake of clarity - are you referring here to the string of zeroes between the decimal place and the first significant digit? Or the string of zeroes after the last significant digit?
I'm referring to both strings; one is infinite, the other isn't. It shouldn't be too difficult, even for grade schoolers, to figure out which.

When you have a repeating decimal, not divicded or multiplied by another number, there's a zero to the left of the decimal point.
There are no zeros after the infinite string of digits (at least that doesn't make sense to me, how about you?).

Following the operation of division by some power of 10 (as long as we're in base 10), zeros appear on the right of the decimal point.

There is a difference between what happens to zero, on the left, or on the right, depending on the operation which, although someone thinks it's a problem to say so, shifts the decimal point. In order for this shift to make sense and follow the "writing rules", we can consider the single zero on the left of the decimal point of a repeating decimal is like an infinite string. I cannot see how this can be hard to understand, seeing it's exactly what anyone who knows how to divide a decimal fraction actually does.

I see 75 pages of posts in this thread. Apparently, there is some kind of simple dispute about zeros before or after a decimal point.

Could somebody briefly tell me what the argument is about, and I'll give you a simple, definitive answer.

Come on people. It can't be that hard.

If Tach has any questions about significant figures, I'm sure I can help there, too.

Following the operation of division by some power of 10 (as long as we're in base 10), zeros appear on the right of the decimal point.

See, it wasn't that difficult to get it right again.

Tach said:
The "dispute" is a side show, arfa brane confused himself on the issue of division by powers of 10 (courtesy of Undefined) but he managed to get it back straight after a few exchanges.
I didn't get confused about division by powers of 10, you fuckhead.

The mistake I made was saying that the zeros ON THE LEFT of the decimal point, for a repeating fraction, are like an infinite string (for the nth fucking time) extending to the right, when I should hace said (for the n+1th fucking time) they extend to the left. This part of my original statement with the mistake in it was not about division, the rest of it was.
But you, being fucking insane, have to pursue it like a fly looking for shit.

You are one fucked up hombre, bro.
See, it wasn't that difficult to get it right again.
I didn't get it wrong, fuckhead. I corrected the mistake I made, which was NOT about what you keep insisting, but that's because you're insane, as well as so fucked up you have to edit someone's post. You lying cunt.

BTW, in case you didn't get it, I don't like you, and I'll be ignoring you, because it's such a waste of fucking time engaging with a prick like you in any way. So get fucked.

Moderator note:

Now, we're all adults here, and I understand that, from time to time, tempers flare, however, I can't say I'm terribly appreciative of having to go through something like 200 posts to weed out 67 trolling, baiting, inflammatory or off topic/administrative posts.

Moderator note:

Now, we're all adults here, and I understand that, from time to time, tempers flare, however, I can't say I'm terribly appreciative of having to go through something like 200 posts to weed out 67 trolling, baiting, inflammatory or off topic/administrative posts.

Dear Trippy,

I'm fairly new here and don't know if it's appropriate to respond with my personal opinion here. That said, I for one favor free speech. I'm a consenting adult and I entered into my participation in this thread. Since it's a frivolous thread (.999... = 1 being an established mathematical fact) there should be very loose moderation standards. You might even say that by attempting to sometimes post serious math in such a thread, I myself am only encouraging the trolls. I already know that .999... threads are pointless. I consider them fun.

I enjoyed my interactions with Tach and participated in them willingly. I for one am disappointed in this action; as it deprived me of one of my daily pleasures.

My principle is: If a forum is going to allow ANY endless discussion of .999... to go on; the discussion might as well be moderated very loosely. The only people on these types of threads are people who enjoy participating in these debates. There's not really all that much difference between posts that are nonsense and posts that are mathematically correct. It's a fun-and-troll thing from the getgo. So you should either lock the thread early; or let it go on. I don't like silencing people whom we've already invited to play.

I apologize if I'm overstepping my bounds by expressing this opinion. But you see, by banning one of the people I was talking to; you deprived me of my opportunity to express the ideas I was discussing with him.

You cannot silence anybody's speech without silencing everybody's speech.

Of course I acknowledge the absolute authority of the site owners to do what they like. This website is somebody's private property. I'm just expressing my feelings about this. Thanks.

Dear Trippy,

I'm fairly new here and don't know if it's appropriate to respond with my personal opinion here. That said, I for one favor free speech. I'm a consenting adult and I entered into my participation in this thread. Since it's a frivolous thread (.999... = 1 being an established mathematical fact) there should be very loose moderation standards. You might even say that by attempting to sometimes post serious math in such a thread, I myself am only encouraging the trolls. I already know that .999... threads are pointless. I consider them fun.

I enjoyed my interactions with Tach and participated in them willingly. I for one am disappointed in this action; as it deprived me of one of my daily pleasures.

My principle is: If a forum is going to allow ANY endless discussion of .999... to go on; the discussion might as well be moderated very loosely. The only people on these types of threads are people who enjoy participating in these debates. There's not really all that much difference between posts that are nonsense and posts that are mathematically correct. It's a fun-and-troll thing from the getgo. So you should either lock the thread early; or let it go on. I don't like silencing people whom we've already invited to play.

I apologize if I'm overstepping my bounds by expressing this opinion. But you see, by banning one of the people I was talking to; you deprived me of my opportunity to express the ideas I was discussing with him.

You cannot silence anybody's speech without silencing everybody's speech.

Of course I acknowledge the absolute authority of the site owners to do what they like. This website is somebody's private property. I'm just expressing my feelings about this. Thanks.
maybe a better place for all this "free" expression " would be in the sub fora "free thoughts".
Freedom of speech does not mean freedom of "soap box" nor does it mean freedom to denigrate or abuse someone.
Whilst I agree with your sentiment, generally the moderators are acting in the best interests of all posters, including those that were the target of a posters post manipulations. [ and the history of behavior associated ] It is important to note that we, as general members, are not privy to the private discussions between moderator and individual member that may have occurred prior to recent banning(s).
Also whilst it may be trivial and a silly thread for some it is a lot more important to others [current and future potential members of sciforums browsing in the background] and a certain emotional investment is made accordingly.

If I was moderating both this post and others that are off topic would be moved to a mediation fora where the poster has to provide justification for the posts reinstatement, thus facilitating forum order and maintaining the freedom of speech.
In this case sciforums has a greater duty of care to the victims of the poster(s) behavior than the rights of the offending member to "freedom to abuse" as distinct from "freedom of speech".

This often abused notion of "freedom of speech" must be clarified as only being available when spoken in a a manner that offers respect to the audience. With out respect there is no freedom.
I expect that this post will be moved and so it should. [as it is off topic]
My apologies to the moderator(s)

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Freedom of speech is not the sole guiding principle on a forum. Economics of making the choice of what type of posts to support requires restricting the speech of some. Indeed, all possible visible abuse, whether it is harassment, bloviation, repeating naked assertions while ignoring the burden of proof or solicitation of human trafficking -- all objectionable activity visible to users is "speech." And when some users have 10+ years of track history of the same or escalating bad behavior, moderation is justified in coming to the conclusion that enough is enough. Moderation here is quite gentle and respectful with discussions happening behind the scenes to provide quality control in decision making; any airing of dirty laundry that I have seen comes from people so egocentric that they want to hash out their disputes in public.

For the most part, there is no upper limit to the sanctions that I would impose on people appearing on the Ban List.

Freedom of speech is not the sole guiding principle on a forum. Economics of making the choice of what type of posts to support requires restricting the speech of some. Indeed, all possible visible abuse, whether it is harassment, bloviation, repeating naked assertions while ignoring the burden of proof or solicitation of human trafficking -- all objectionable activity visible to users is "speech." And when some users have 10+ years of track history of the same or escalating bad behavior, moderation is justified in coming to the conclusion that enough is enough. Moderation here is quite gentle and respectful with discussions happening behind the scenes to provide quality control in decision making; any airing of dirty laundry that I have seen comes from people so egocentric that they want to hash out their disputes in public.

For the most part, there is no upper limit to the sanctions that I would impose on people appearing on the Ban List.

I am not seeing in this thread where you proved you can concatenate an infinite collection of digits of .9999(n) for every n.

Since, at any n, there is a finite number of digits and an infinite collection of digits yet to go this needs to be justified.

That is why this thread is still going on.

Do you have said proof or any justification?

Rational Does NOT = Irrational

rational finite( 1 ) does not equal irrational infinite 0.999 .....
non-counting( 0 ) does not equal irrational infinite 0.111....

0.999...= infinite irrational

1.0000 = finite rational

0.111..... = an infinite irrational

1.0 = finite rational

Those who believe irrational and rational are = to each other are playing illusionary mathematical games with no correlating basis in reality.

Those who claim that the irrational 0.999.... = 1.0 cannot offer any proof of such using a simple rational, logical explanation and only can offer us extremely complicated maths and rarely known complicated mathematical terms to even begin to expressed their alledged proofs.

I believe they have no proofs and using hand waving mathematical illusions to fool those of us who request simple, rationallu logical common sense explanation that common person could understand, with a litte help. They have nothing of the sort to offer us, so even those who really are clueless begin to accept their complicated mathematical illusions, because........?

There is no good reason to accept there given extremmely complicated mathematical illusions.

Please share when any one actually has a simple, rational, logical and common sense explanation of how 0.999... is = to 1.0.

I will not be holding my breath for that one.

r6

0.999...= infinite irrational

1.0000 = finite rational

0.111..... = an infinite irrational

1.0 = finite rational

Those who believe irrational and rational are = to each other are playing illusionary mathematical games with no correlating basis in reality.

Those who claim that the irrational 0.999.... = 1.0 cannot offer any proof of such using a simple rational, logical explanation and only can offer us extremely complicated maths and rarely known complicated mathematical terms to even begin to expressed their alledged proofs.

I believe they have no proofs and using hand waving mathematical illusions to fool those of us who request simple, rationallu logical common sense explanation that common person could understand, with a litte help. They have nothing of the sort to offer us, so even those who really are clueless begin to accept their complicated mathematical illusions, because........?

There is no good reason to accept there given extremmely complicated mathematical illusions.

Please share when any one actually has a simple, rational, logical and common sense explanation of how 0.999... is = to 1.0.

I will not be holding my breath for that one.

r6

This is a good argument.

You are forcing the proof that an irrational number is a rational number in order for .9999999999....=1 to be true.

This is the simplest I have seen so far.

This cannot be beat.

0.999...= infinite irrational

1.0000 = finite rational

0.111..... = an infinite irrational

1.0 = finite rational

Those who believe irrational and rational are = to each other are playing illusionary mathematical games with no correlating basis in reality.

Those who claim that the irrational 0.999.... = 1.0 cannot offer any proof of such using a simple rational, logical explanation and only can offer us extremely complicated maths and rarely known complicated mathematical terms to even begin to expressed their alledged proofs.

I believe they have no proofs and using hand waving mathematical illusions to fool those of us who request simple, rationallu logical common sense explanation that common person could understand, with a litte help. They have nothing of the sort to offer us, so even those who really are clueless begin to accept their complicated mathematical illusions, because........?

There is no good reason to accept there given extremmely complicated mathematical illusions.

Please share when any one actually has a simple, rational, logical and common sense explanation of how 0.999... is = to 1.0.

I will not be holding my breath for that one.

r6

The value of 1 is made up of what?
How do we go from zero to one?

Chinglu, you are mistaken -- I do not need to concatenate an infinite number of 9's to form 0.999... because by assumption the digits in 0.999... are always 9 and already exist at all positions right of the decimal point.

Because of the axiom of completeness for the real numbers, the following holds true for the non-negative real numbers.

$${a_0.a_1a_2a_3\dots}_{\tiny 10} \quad = \quad \sum_{k=0}^{\infty} \frac{a_k}{10^k} \quad = \quad \textrm{sup} \; \left{ x : \; \exists n \in \mathbb{N} \; \wedge \; x = \sum_{k=0}{n} \frac{a_k}{10^k} \right} \; = \; \lim_{n\to\infty} \sum_{k=0}^{n} \frac{a_k}{10^k} \; \in \; \mathbb{R}$$

Therefore $$0.999... = \quad \textrm{sup} \; \left{ 0, \, 1 - \frac{1}{10}, \, 1 - \frac{1}{10^2}, \, 1 - \frac{1}{10^3}, \dots \right} = 1$$.

This follows from continuity and monotonicity of the exponential because $$\forall k\in \mathbb{Z} \; \frac{1}{10^{k+1}} \lt \frac{1}{10^k}$$ and so if $$0 \lt 0.999... \lt 1$$ then $$n \quad = \quad 1 - \left\lfloor \log_{\tiny 10} \left( 1 - 0.999... \right) \right\rfloor \quad \in \mathbb{N}$$ and therefore $$1 - \frac{1}{10^{n-3}} \lt 0.999... \lt 1 - \frac{1}{10^n} \lt \textrm{sup} \; \left{ 0, \, 1 - \frac{1}{10}, \, 1 - \frac{1}{10^2}, \, 1 - \frac{1}{10^3}, \dots \right} \lt 0.999...$$ which is a contradiction that proves $$0.999... \not\lt 1$$.

This is a good argument.
That is not an argument at all. In [post=3139661]post #1453[/POST], rr6 nakedly asserts certain numbers are irrational without a demonstration.

... 0.1111..... = an infinite irrational...r6
It is 1/9 and that is a frational fraction.

Chinglu, you are mistaken -- I do not need to concatenate an infinite number of 9's to form 0.999... because by assumption the digits in 0.999... are always 9 and already exist at all positions right of the decimal point.

Because of the axiom of completeness for the real numbers, the following holds true for the non-negative real numbers.

$${a_0.a_1a_2a_3\dots}_{\tiny 10} \quad = \quad \sum_{k=0}^{\infty} \frac{a_k}{10^k} \quad = \quad \textrm{sup} \; \left{ x : \; \exists n \in \mathbb{N} \; \wedge \; x = \sum_{k=0}{n} \frac{a_k}{10^k} \right} \; = \; \lim_{n\to\infty} \sum_{k=0}^{n} \frac{a_k}{10^k} \; \in \; \mathbb{R}$$

Therefore $$0.999... = \quad \textrm{sup} \; \left{ 0, \, 1 - \frac{1}{10}, \, 1 - \frac{1}{10^2}, \, 1 - \frac{1}{10^3}, \dots \right} = 1$$.

This follows from continuity and monotonicity of the exponential because $$\forall k\in \mathbb{Z} \; \frac{1}{10^{k+1}} \lt \frac{1}{10^k}$$ and so if $$0 \lt 0.999... \lt 1$$ then $$n \quad = \quad 1 - \left\lfloor \log_{\tiny 10} \left( 1 - 0.999... \right) \right\rfloor \quad \in \mathbb{N}$$ and therefore $$1 - \frac{1}{10^{n-3}} \lt 0.999... \lt 1 - \frac{1}{10^n} \lt \textrm{sup} \; \left{ 0, \, 1 - \frac{1}{10}, \, 1 - \frac{1}{10^2}, \, 1 - \frac{1}{10^3}, \dots \right} \lt 0.999...$$ which is a contradiction that proves $$0.999... \not\lt 1$$.

1) Can you show this axiom of completeness under ZFC set theory? Otherwise, you would need to prove that from the axioms. You did not.

2) You showed an infinite summation operator above. There is no such thing as infinite summation. There is only an infinite sequence of partial sums, each element of the sequence is finite for all n. This is well known.

Now can you prove from ZFC your assertion that such an infinite summation operator exists? This is on you.

Also, for all n, every time you claim you are getting close to 1, I have a neighborhood around 1 that is closer to 1 than your sequence of 9's. This never ends. What do you do about this?

That is not an argument at all. In [post=3139661]post #1453[/POST], rr6 nakedly asserts certain numbers are irrational without a demonstration.

OK, can you prove the irrational .9999.. is a rational number being 1? That is the issue.