[split] 0.999... equals 1

[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