Originally posted by: DrPizza
Originally posted by: bleeb
Proof by induction:
Given 0.9 != 1.
then
0.99 != 1.
0.999 != 1.
0.9999 != 1.
0.99999 != 1.
We conclude that
0.9999... != 1.
WHO'S YO DADDY?!
A proof similar to yours:
1 !=10
1+1 !=10
1+1+1 != 10
1+1+1+1 != 10
you conclude that 1+1+1+1+1+1+1+1+1+1 != 10
Your proof is just as absurd, except you don't recognize it as such.
Proof by induction is a valid method of proving things, and can be used to prove mathematical statements that couldn't be proved by the method of exhaustion (when there are an infinite number of possibilities). However, labeling your proof "proof by induction" does NOT make it a proof by induction, nor does it make it valid.
Here's one that's closer to yours that *maybe* you'll recognize is wrong:
.3 != 1/3
.33 != 1/3
.333 != 1/3
.3333 != 1/3
.33333 != 1/3
.333333 != 1/3
.3333333 != 1/3
.33333333 != 1/3
therefore .333... != 1/3
"proof by not paying close enough attention in math class"