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Originally Posted by Michael Hill
In the second step when you multiply it by 10, you will get soemthing like 9.9999.....0. There must be a 0 on the end. This is because there are no longer infinity 9s at the end. There are infinity minus 1.
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You don't get a zero on the end when you multiply .9999... by ten. The 9s
never run out.
Infinity minus one is exactly the same as infinity. You can't do simple arithmetic like subtracting one with inifinities; they are defined as larger than any number. You can't get away from infinity by subtracting finite values unless you subtract an infinite number of them.