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Proof by induction

Ok, just a quick question really...

I know you usually prove it for say, n = 1..then assuming true for n=k, show this means it is true for n=k+1.

But, could you prove true for n = 1, then assume true for n is less than or equal to k, and show this means it is true for n = k+1? Thinking about it I think it's ok, since it would be true for n = 2, then n = 3, etc. but I haven't seen it in this way before!

Thanks!
Original post by Z1G
Ok, just a quick question really...

I know you usually prove it for say, n = 1..then assuming true for n=k, show this means it is true for n=k+1.

But, could you prove true for n = 1, then assume true for n is less than or equal to k, and show this means it is true for n = k+1? Thinking about it I think it's ok, since it would be true for n = 2, then n = 3, etc. but I haven't seen it in this way before!

Thanks!


This is known as "strong induction" or "complete induction", and is perfectly valid. Have a quick Google.

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