Quote (Phils_Porsche @ 6 May 2010 16:00)
Let x be 0.999...
10x=9.999...
10x-x=9.999... - 0.999...
9x=9
x=1
9x -x = 8x = 9- .999999..... = 8.0000.....001 = 8( .999999....)
Is that what you're also going to tell me? You're trying to prove .999.... = 1, you can't assume it from the very beginning.
That "proof" isn't rigorous at all. I thought you were good with this logic stuff?
As I mentioned earlier - there's no such thing as ... and then a number, as far as I know. Saying "After infinity, put this digit" is utterly meaningless.
I didn't say it was particularly rigorous, I just said it was correct and I had yet to see anyone poke a hole in it. If someone can poke a hole in it, then we can go with something with more rigor.