I like dividing by 9...
1/9 = 0.111111...
2/9 = 0.22222...
3/9 = 0.33333...
4/9 = 0.44444...
5/9 = 0.55555...
6/9 = 0.66666...
7/9 = 0.77777...
8/9 = 0.88888...
9/9 = 0.99999...
Is there a problem in that sequence?
I see one! ;)
Nope. It can be proven in real analysis that 0.9999999...=1. It is customary to use decimal representations with infinitely repeating zeros rather than infinitely repeating nines, but the two are equal. 1=1.0000... - hence infinitely repeating zeroes rather than the equivalent 0.999999....