Entroper on 01 June 2007
You can't prove something by assuming that it's true. You can disprove something by assuming that it's true, and then reaching a contradiction, that's a proof by contradiction.
If you're doing a proof by contradiction, you have to reach a contradiction.
In this example, if you assume that .9999... and 1 are not the same number, then you can use (.9999... + 1)/2 to show that there exists a number between .9999... and 1, but this is not a contradiction, so it neither proves nor disproves anything.
I'm just trying to state this clearly so that it's understandable, not trying to say "YOU'RE WRONG!" When I said that the average "doesn't work" I meant that it doesn't prove or disprove that .9999... = 1, not that it doesn't give you a number.
