Re: Simple versus formal proof?

Ross Clement (Email address invalid - do not use) wrote:
Mohab wrote:
not so, what if you go negative?
(k-1)^2 + (k-1)

// snip

it really shows up how proof by induction is unneccessary for this problem,
> but it would still be a valid proof by induction would it not?

Yes. Mohab is completely wrong here.

It's quite a sweet proof, and every bit as valid as the "k or k+1 must be..." one. (Anything that starts with "1 + 1 = 2" gets my vote!). If you're struggling with a problem, any proof will do! (In my experience, once you've got any proof down, however horrible, then you often start understanding better *why* what you've proved is true, and then more elegant proofs follow). But in any case yours is, as I said, pretty nice.

But the "if 2 divides X * Y then 2 divides X or 2 divides Y (or both)" trick is quite useful, and generalises quite a long way. (How far?). Don't forget it...


Tom
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