Asked my college calculus professor about this today, and he said that
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.9 does equal 1. He explained it this way.
1/9 = .1 repeating...
2/9 = .2 repeating
3/9 = .3 repeating
4/9 = .4 repeating
5/9 = .5 repeating
etc etc....
8/9 = .8 repeating
9/9 = 1.
Whether that is the actual proof