A Conversation for Basic Methods of Mathematical Proof


Post 1

Martin Harper

Proof by blatant assertion: heh - I had that in my text book - the guy wrote "by induction and blatant assertion, " - but that's the only time I've seen it... perhaps most people aren't so honest...

Of course, no proof by blatant assertion is complete without "clearly", "obviously", or some other word designed to make the reader feel stupid. smiley - smiley

Proof by induction - well you simplified here, I suspect deliberately - there's weak induction, which is what you've got here - but then there's strong induction, which is where you show that if true for n<k, then true for n=k - and works for more than integers - if I recall, it's any "wellfounded" set - or some such nonsense. And there's structural induction, which is what I seem to be spending half my life doing at the mo...

Got a project opening for an entry on induction? smiley - winkeye

Oh, and finally, you missed the rather key method of proof - which just uses stuff like "if A implies B, and A is true, then B is true" and "if A implies B, and B implies C, then A implies C" - and do this until you've shown that X is true, where X is what you want to prove. This has a fancy name, too - but I can't recall what it is. Comes in forward and backwards variants too... oh for a new memory smiley - sadface

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