[split] 0.999... equals 1

[fr0d0]

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

If there could be a logical definition of infinity minus infinitesimally small that would be the number. As infinity can be no real number it's crazy to apply real number logistics to it.

Fact remains.. the 2 can never converge, no matter that you can't name the infinitesimal, we know it's there at every stage. There is no end to infinite.. so the infinitesimal amount has no end either. Just because I can't name the number doesn't mean it doesn't exist. We KNOW it HAS to exist using logic. the logical proofs deny this, which is their error.

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.

I know I just felt sorry for C all here alone

Nothing wrong with questioning is there?!?


Say you had an infinite railway line. You know the line moves closer to the border 9/10ths every mile. On your (incredibly short but long haha! ...this would have to be an incredibly shrinking train and track! LOL) train journey, at every mile you notice the gap decreasing by 9/10ths... but it NEVER reaches 10/10ths at any point. It cannot, because we've already established that it keeps to 9/10ths to infinity, the law says so.. "no train track shall ever touch the damn border!!!" (damn politicians!!)

[Retorth]

I really do wonder...if the maths already proves itself, why is it so hard for some people to accept? :S


1/3 = 0.3r
2/3 = 0.6r
3/3 = 0.9r = 1


if X = 0.9r

10X = 9.9r
10X - X = 9.9r - 0.9r
9X = 9
X = 1

[Eilonnwy]

I really do wonder...if the maths already proves itself, why is it so hard for some people to accept? :S

Part of me wonders if it's not so much a lack of understanding the math but inability concede the argument. *shrugs*

[leo-rcc]

I really do wonder...if the maths already proves itself, why is it so hard for some people to accept? :S

Part of me wonders if it's not so much a lack of understanding the math but inability concede the argument. *shrugs*

Okay that is not fair. She is in the exact same state as I am, there have been a lot of figures thrown around but none of them have even remotely convinced me in the slightest that a value less than 1 equals 1.

0.3r is not 1/3, it is an approximation as close to 1/3 you can get in decimals. 0.1r is not 1/9 in decimals but an approximation. If you then start to calculate with those figures as being accurate, you get errors.

If these are the proofs you all hang on to fine, I won't argue them. But because I do not accept the proofs laid before me because I question the methodology used that is not the same as an inability to concede an argument.

[Edwardo Piet]

If there could be a logical definition of infinity minus infinitesimally small that would be the number. As infinity can be no real number it's crazy to apply real number logistics to it.

We're not talking about infinity itself, but an infinite - an endless- stream of 9s recurring on the end of 0.9, so there can be no number between it and 1, so it=1

Fact remains.. the 2 can never converge, no matter that you can't name the infinitesimal, we know it's there at every stage. There is no end to infinite.. so the infinitesimal amount has no end either. Just because I can't name the number doesn't mean it doesn't exist. We KNOW it HAS to exist using logic. the logical proofs deny this, which is their error.

No, we knot that it logically can't exist. Because - using logic - there can be no number between 0.9r and 1 because there is no gap between them because the 9s on the end go on for infinity. It's not a matter that you can't name it, it's a matter of the fact that it logically can't exist - not that it logically has to! It can't!

The logical proofs deny what? Deny the fact that according to you there can be a number between 0.9r and 1 when there logically can't because there can be no number between them?

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.

Say you had an infinite railway line. You know the line moves closer to the border 9/10ths every mile. On your (incredibly short but long haha! ...this would have to be an incredibly shrinking train and track! LOL) train journey, at every mile you notice the gap decreasing by 9/10ths... but it NEVER reaches 10/10ths at any point.

we're not talking about anything 'reaching' anything. 0.9r doesn't have to reach 1, it's a matter that it logically must be the same number represented in decimal: Because there can't logically be a number between it and 1 because the 9s on the end of 0.9r go on for infinity!

It cannot, because we've already established that it keeps to 9/10ths to infinity, the law says so.. "no train track shall ever touch the damn border!!!" (damn politicians!!)

Infinity is not a number so you can't have 9/10s of it, that's a different matter. We are not talking about infinity itself, but an infinite number of 9s recurring on the end of 0.9.

Okay that is not fair. She is in the exact same state as I am, there have been a lot of figures thrown around but none of them have even remotely convinced me in the slightest that a value less than 1 equals 1.

But that's just it, it's not at all that a number less than 1 is equal to 1. The point is that 0.9r is not less than 1 in the first place. Because 0.9r has an endless number of 9s on the end of it, recurring to infinity, and so you can't put anything on the end of it. There can logically not be any number in between it and 1, and so it logically must be the same number represented in decimal.

EvF

[leo-rcc]

And so because of the inability to get the number accurate in decimals (otherwise you would not have this recurrence to begin with) you just make that out as being equal. I don't accept that as logical at all.

[Edwardo Piet]

There can't be any number that is any more or less in amount than it, so it must logically be the same number.

The decimal system is one way we represent numbers. Numbers are man made concepts anyway.

I mean you could say that there's a number called PQ175 that transcends the decimal system and was more than 0.9r but less than 1 but I don't see that as logical. 0.9r is a representation of 1 in decimals - because there can't be a number in between it and 1 - in our own understanding as humans, of what numbers mean/are.

EvF

[leo-rcc]

But those numbers represent values, and if a system of representing those values are inadequate either concede that they are the best approximation possible or find another numerical system that works. If you think that 0.9r=1 is logical, fine, but those that do not are not automatically stubborn idiots because they don't see it your way. That is a theistic bullcrap argument.

[Tiberius]

I'm sorry leo, but 0.3r is equal to 1/3. You can prove it easily with long division and induction.

So either long division is wrong, induction is wrong, or your assertion is wrong. Unfortunately for you, both these methods are provably correct, leaving only your assertion being wrong as the answer.

You say you aren't convinced that a value less than 1 equals 1. Well obviously you aren't, and neither are we. 0.9r isn't less than 1, it is the same as 1. You have been brought up to think that any number with a prefix of 0. must be less than 1. The point is, that is a linguistic mistake, not a mathematical one. The fact is, you can represent the same value in multiple ways in the decimal system. That is all.

[Edwardo Piet]

@ Leo For the record, I don't think that anyone here is a stubborn idiot for not accepting the matter. That was never my position.

Well since there can be no number between 0.9r and 1 then that's why it's 1 represented in decimal. just as 5/5 is 1 represented in fractions despite it being different digits.

( clicked reply just after Adrian did).

EvF