[split] 0.999... equals 1

[fr0d0]

You answer first...

[Edwardo Piet]

I already disagreed...

I already said that I think they converge in the sense I said above, and have said more than once........

Ok, your turn to answer now...

EvF

[fr0d0]

I agree in a sense. I can see how it's justified. I also have objections for the reasons specified. I think it's ok to be open minded and keep questioning. To re-visit and think of proofs/ disproofs and test those.

[Edwardo Piet]

What do you mean 'in a sense', it has been logically proved, right?

It can't be more or less than 1, so it logically must be 1 represented in decimal.

Counter-intuitive? Yes. Does it make logical sense? Yes.

EvF

[fr0d0]

It cannot be more than one, it can be less than one. That is unless you take a leap of faith.

[Edwardo Piet]

It can't be less than one, because there's no gap between it and 1, because there can't be a gap between 0.999999999999r - with an endless string of 9s, endless - and 1.

EvF

[fr0d0]

So you're saying they touch. We don't have a descriptor for the gap therefore we state that they touch, even though we know from the proof above that they cannot. Ever.

The line from 0.9 to infinity isn't straight. It's a curve away from 1, never ever hitting one.

[Edwardo Piet]

No it's not that we don't have a descriptor. It's that there can't possibly be a gap between them because you can't add anything onto an infinite, never-ending... - an endless string of 9s in order to make it 1. So it can't be any "less", because there is no gap between them.

EvF

[Tiberius]

Damn, what happened fr0d0? I thought you got this a dozen pages back?

It has nothing to do with convergence. 0.9r (or 0.9... or whatever) is just another way of writing 1 in the decimal system. You say 0.9r can be less than one. Ok, that's a testable claim. Please tell me the number that you can add to 0.9r to make it 1.

[Tiberius]

If infinity is not a value at all, then the value of 0.9^ is 0.9. You are using the concept of infinity to describe the value of a number, and in doing so make that number's identity uncertain... Impossible to calculate. I do not see where I contradicted myself in this instance.

We are using the concept of infinity to describe the number of 9's in the number. It tends to infinity. Infinity isn't a number, and I have shown proof of that. When we say "tends to infinity", we mean it goes on forever with no end. The ^ on the end of 0.9^ means that the previous set of numbers repeats forever. It's a mathematical concept known as "infinity", it is not a number.

So you are saying that 1/0 and 2/0 can be calculated? If something takes an infinite amount of time to calculate, it is because it is incalculable. We call these numbers 'undefined'. What is the answer to 1/0? Undefined. Oh wait... that would be calculable because it only takes an infinite amount of time to calculate? lol?

No, 1/0 and 2/0 cannot be calculated, namely because 0 goes into 1 an infinite amount of times and infinity is not a number (see previous proofs), so there is nothing to calculate. 0.9r is a number, and is hence calculable.

Yes, I read the entire article. All the way down to this quote, which I posted before, probably with hide tags like I am doing now

That quote still didn't address my point, which was that there is no such thing as an 'infinith' item of an infinite set. This was what the word 'infinitesimus' (from which infinitesimal is derived) used to mean, not what it does now.

Yes, I read that it was the original description of it... yet surly you should know that it was under that description that Calculus was invented.

Anyway, I did discuss this subject with several mathematicians. Instead of calling me a moron (among other things): Target my arguments and statements. Am I calling you a moron in my dissent of your arguments? Not that I can tell. Do I suggest that you haven't researched this subject? Also not that I can tell. Have you proven to me yet that this inequality is equal? You have not.

My apologies, my original post should have made it clear that it was the word 'infinitesimus' that meant 'infinite-th'. The word's meaning was then changed, and became infinitesimal. So yeah, to clarify, infinitesimal never meant 'infinite-th'. I do target your arguments and statements; you repeatedly fail to make a dent in mine, and then ignore my rebuttals and stride onwards with new "proofs". I have provided proofs that you have failed to disprove. Just because you do not accept them as proof does not mean they aren't. Point out the mathematical flaw in the proof, and we can discuss it. Every time you have tried to do so, you commit fallacy after fallacy, and make basic mathematical mistakes. Me insulting your apparent inability to do math is what keeps me sane in this discussion.

I would like to do so if you continue to not prove your statements. I told you before that I don't doubt that the mathematicians are right... I simply have to make it right by me. As of yet: I do not see it. Why wouldn't you ask questions of mathematics to mathematicians?

I have proved my statements, multiple times with multiple proofs. You have failed to disprove them, and resort to bad math when trying. I don't understand how you can still be going with this when I've continually pointed out the mistakes you've made. Are you actually capable of admitting you are completely wrong, or is this a pride thing? If you want to admit you are wrong and not hurt your pride, PM me. I won't tell anyone, we'll just let this discussion sink down the results page...

limitless or endless in space, extent, or size; impossible to measure or calculate

Can something be infinite only in size? Open your mind. .9^ is infinite in length. oo is infinite in size. Arrogance can be infinite in sheer incalculability. Seriously... and honestly... infinite is an adjective... it is not a noun. When you modify a value you sticking infinite on it: you have made that value impossible to calculate. Finites are not impossible to calculate, so from the very beginning .9^ CANNOT equal 1... lest an infinite be finite which would declassify it's infiniteness.

This is my proof, the proof of the Identity's Equality (That I am me and not you... remember?). Only by canceling out that which cannot be calculated can we calculate.

Perhaps before saying things are 'infinite' you should clarify which kind of infinite you mean in future then. Saying 0.9r is infinite could mean many things, infinitely large, infinitely long, infinite as the actual concept. Only one of them is correct. So by your definition, PI is incalculable? Darn…we're going to need some new geometry rules. We can calculate infinitely long rational numbers, and we can calculate irrational numbers to a certain degree. Infinitely long rational numbers can be calculated by induction (i.e the long division of 1 divided by 3).

Only for finites. This only applies to the incalculable. Referring to what I said above: If you cancel out the infinite, then you have made the number finite, and are no longer proving an infinite. Unless you are suggesting that infinities are finite? Or that there really IS an answer to 1/0?

By canceling out impossible to solve things, you make equations solvable. Thus you can get your answer to the equation via this method. So you are not proving that an infinite is equal to a finite... you are proving that the remaining equation (now that you have removed that troublesome infinite) is equal to a finite

Yet we aren't cancelling out the infinite, we are doing simple subtraction. 1.2 - 0.2 = 1. We've 'cancelled out' the .2, yet this sum works. Now if you use induction, you can show that the same applies for every increment of this, like so:

1.22 - 0.22 = 1
1.222 - 0.222 = 1
1.2222 - 0.2222 = 1

This is a proof by induction, and it works fine.

And you can't have an infinitely long penis... with a head? The number on the 'end?' is a descriptive quality to the number, insomuch as the head is a descriptive quality to the penis. Lest the number be non-descriptive (like 1/0?), you must include those describing digits.

Funnily enough, I have gotten my proofs of different answers from 10x-1x vs 9x by a calculator. With finite numbers: you're fine. With incalculable infinites? Not so much.

No, you can't have an infinitely long penis with a head. The head is the end of the penis, and the penis you have defined as infinitely long…without an end. The number "on the end" is meaningless; it can't exist.

Etc. Please understand that infinity is the value of endlessness, unfathomability. It is he value of being without limit. Using it to describe a number (see .9^) is removing that number from being limited... making the fathomable decisively not. Numbers like .0^1 are to show that there is an unfathomable, limitless number of zeros before a one. This is not an infinite number with an end... it is a finite number placed unfathomably in the distance.

Numbers like .0^1 are meaningless. How can you have a limitless number of zeros before a one? By saying the one exists, you are immediately giving the number of zeros a limit. Either the number of zeros is finite (and so not infinite), or the '1' can never be placed, and so it is not needed at all (and is meaningless). Please, point out the flaw in my logic if you think there is one, but you are making one epic contradiction.

Haha we have to make a leap of faith and just accept that 0.999... = 1. It's the language of math and is defined provably so. Yet a simple counter is that 0.999... is smaller than 1. The onus is on those who state the positive.

The onus is on you since you have not disproved the proofs presented, only made logical fallacies in your own attempts. If 0.999… is smaller than 1, give us the number that fits snugly between them! Simple really!

Yeah, I agree with ConMan on that one, whether the infinite number is 8.9999999..1 or 9.99999.., the two sides of the algebraic equation remain equal, but c still doesn't equal 1. My algebra is very rusty, that said, the only problem I see is with the algebraic equation as provided by ConMan, where Step 3 is written as 9c = 9. This is incorrect. It should be 9 = 9. Step 1 is: (10 * c) - c = 9.999.. - c; So we process (10 * c), resulting in 9.999... and then removed c from both sides of the equation, leaving 9 = 9, not 9c = 9. Well, you can do this with any variable.
10x = 40.
10x - x = 40 - x.
36 = 36.
36/36 = 36/36.
x doesn't equal 1, x = 4.
Nor is c equal to 1, c = .999...
lets say that x = 0.999...
multiply both by 10 10x = 9.999...
take the first from the second 9x = 9
and divide by 9! x = 1
There fore, 1 = x = 0.999... If you want further proof that .999... != 1, try getting 1 to equal .999... hah = )
This was great fun though, thanks = )
As much as I'd like to disprove this, I'm afraid the above method isn't entirely correct. The algebra is flawed. If you have 10c = 9.9999 and you take away a c (10c - c = 9.9999 - .9999) you are left with 9c. Not 9. Just as if you had 10c and took away 4c you would have 6c and not 6. In order to get 9 from 9c you would have to divide by c, not subtract (10c / c = 9.999 / c which would be 10 = about 10 although not EXACTLY 10 since in order for a divided number to equal itself the number needs to be 1 which .999 is not)

A number of the 're-proofs' to the disproofs on that page a quite flawed, so far as I can tell.

That proof is completely flawed. He starts out fine (my comments are after the // )

10x = 40. // Fine, set 10x to 40, so x is equal to 4.
10x - x = 40 - x // Fine, subtract x from both sides, simple algebra.
36 = 36. // Excellent, so 36 = 36.
36/36 = 36/36 // Good, so he's dividing each side by 36.
x doesn't equal 1, x = 4. // Eurggggh.....

*facepalm*

YOU JUST GOT RID OF THE X BY SUBSTITUTION!

You know, that step where suddenly the x disappears and is replaced by 36 on each side…that happen because you know x is 4 and you decided to put it back into the equation! By saying 36/36 = 36/36, you are not saying x = 1, you are saying 1 = 1…which is perfectly true!