1 = 0,99........

[Ghieri]

For how can you end an "infinite" with "01" and still call it "infinite"?

We are talking about infinitely small numbers, which have to have their "last" digit as 1. My point is that the infinite number of zeroes never reach that point. Therefore, infinitely small.

Thankfully, "..." doesn't necessarily mean "infinite," in which case 0.99...9 != 1.

We are not talking about measurably small numbers, so "..." does not equal a finite number of places in this case. If "..." were a finite number of places then I would agree. But it isn't.

Is that to say that prominent mathematicians fail at logic or that you aren't a mathematician?

I'm not really sure what I did that put a stick up your ass, but whatever it is probably isn't relevant to the discussion. Anyways, there are several mathematical proofs on the topic:

n = .99~

10n = 9.99~

10n-n = 9n

9n = 9
n = 1

1/9 = .11111~
9(1/9) = 9(.11111~)
1 = .99999~

More here.

So while it seems counter intuitive. It is mathematically solid.