.999999 = 1

If they equal they aren't two different things. They are two of the same thing.

you guys are fucking annoying

if two numbers are unequal, then there exists other numbers between them

find a number between 0.999.... and 1

there isn't one. since there are no numbers between the two of them, they are the same

0.999.... = 1

>if two numbers are unequal, then there exists other numbers between them
prove it faggot

there is a number between them tho
0.9999.... + 0.1111....

If [math] x \neq y [/math] then either [math] x < y [/math] or [math] x>y [/math]. Take the former case then: [eqn] 2x < x+y \implies x < \frac { x + y } { 2 } \\ \text { Likewise } ~ x + y < 2y \implies \frac { x + y } { 2 } < y \\ \therefore x < \frac { x + y } { 2 } < y [/eqn]

should have left it as an exercise to the brainlet

Probably. But I'm procrastinating.

An infinitely re-occuring decimal can actually be the same as a finite number.

>1.111... is between 0.999... and 1

You don't say, Sherlock!
n.000...=n