0.9999.... is equal to 1

I honestly thought that by this time, everyone in the world knew this was true, save those who have absolutely no idea what numbers are.....ok, I'll do my best to explain this to all you would-be trolls.

1/3 = 0.333
now multiply both sides by 3 and you get:
3/3 = 0.9999....
OR
1 = 0.9999....

Now, Let's start with 1 = 0.99999.... this time.
Subtract 0.9999.... from each side and you get:
0 = 0.00000....
Yes, there is a 1 there, but it is exactly aleph null zeros from the decimal.....meaning it kinda isn't there, and that you just subtracted the same number from two numbers and got the same answer for both....thus they must be equal.

Last: between any two unequal real numbers, there are infinitely many numbers. I'd like to challenge anyone to find a number between 0.9999..... and 1. If you can find that number, then you win infinitely many internets, but if not, just admit that 0.999... does, in fact, equal 1.

>>32
Eep.  You fucked up.  It is possible to have two different irrational numbers that do not have an intervening fraction, but that doesn't mean two different irrationals are equal.