- #1
homology
- 306
- 1
I was surprised when a few months ago, while talking to a fellow student, he suggested that the way you prove an equality (like P=Q) is you start with P=Q and play with it until you get something that's true, then you "know" that P=Q is true.
Now this is rubbish of course, since a false premise can imply a true one. And I showed him the example:
2=1 subtract 1 from both sides
1=0 add 1 to the left and 2 to the right to get
2=2
But he scoffed and said, "sure, sure" but you're using what you're trying to prove (the fact that 2=1). Well its clear that I haven't made him a believer, I was wondering if any folks here had really juicy examples of trying to prove P=Q, a false statement and ending up with R=S, a true one.
Thanks a lot,
Kevin
Now this is rubbish of course, since a false premise can imply a true one. And I showed him the example:
2=1 subtract 1 from both sides
1=0 add 1 to the left and 2 to the right to get
2=2
But he scoffed and said, "sure, sure" but you're using what you're trying to prove (the fact that 2=1). Well its clear that I haven't made him a believer, I was wondering if any folks here had really juicy examples of trying to prove P=Q, a false statement and ending up with R=S, a true one.
Thanks a lot,
Kevin