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Im wondering if this template for induction would be valid

show true for n=1

assume true for n=k

Attempt to show true for n=k+1

but at this point just replace n with k+1 and dont use the assumption that n=k.

show that the expression with n replaced by k+1 is equivalent to the one assumed for n=k.

Basically i have been asked to figure out if this is ok. My thoughts are

They assumed it for n=k ok

Then they showed it for n=k+1. Here i think what they have done is shown if true for k+1 then true for k.

But i guess it works the other way so i think its ok.

Any help would be appreciated, thanks

hitherematey
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  • It does not work the other way around. Suppose $S(n)$ is "$ n=1$". Then $S(1)$ is true. And for all $n\in \Bbb N$ we have $S(n+1)\implies S(n).$ But it is obviously not true that $\forall n\in \Bbb N,(S(n)).$... Forget about $k$. There is only one variable ($n$) to consider. – DanielWainfleet Nov 17 '18 at 08:01

1 Answers1

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Assume true for n=k.

Attempt to show true for n=k+1.

Never mind "attempt." You must do it. Show true for n=k+1 using your assumption for n=k, and you will be done.

But at this point just replace n with k+1 and don't use the assumption that n=k.

This would be a waste of time. You would simply be making another assumption and proving nothing.

Tip: If you are stuck after proving true for 1, prove it true 2, 3 and 4 as well. This may help you to better understand the problem.

Community
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Dan Christensen
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