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.(adsbygoogle = window.adsbygoogle || []).push({});

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 statment and ending up with R=S, a true one.

Thanks a lot,

Kevin

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# 0=1 proof

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