This is very old, but I haven't heard about it before.

1 == 0.999...

It can be proven in two ways:
1
1/3 = 0.333...
1/3 * 3 = 0.333... * 3
1 = 0.999...


2
x = 0.999...
10x = 9.999...
10x - x = 9.999...- 0.999...
9x = 9
x = 1

Sorry if this has been posted before, but I couldn't find it (The search here is not good, it never finds anything, so it might be that I missed it).

If you don't believe me, have a look here