Name: Anonymous 2011-09-10 16:20
Proof # 1:
Assume .9999... = 1
Then that means .999... = .999..8
Then that means .999...8 = .999...7
And so on until 1 = 0
However 1 =/= 0
So by proof of contradiction we have proved .9999... =/= 1
Proof # 2:
Assume .999... = 1
Multiply both sides by 10000...
Then we get 99999... = 100000...
However 10000... - 99999.... = 1
1 > 0
Therefore 1 =/= 0
Since the difference is not 0, we conclude .99999...=/= 1
Assume .9999... = 1
Then that means .999... = .999..8
Then that means .999...8 = .999...7
And so on until 1 = 0
However 1 =/= 0
So by proof of contradiction we have proved .9999... =/= 1
Proof # 2:
Assume .999... = 1
Multiply both sides by 10000...
Then we get 99999... = 100000...
However 10000... - 99999.... = 1
1 > 0
Therefore 1 =/= 0
Since the difference is not 0, we conclude .99999...=/= 1