I'm trying to find an example of a statement S(n) that is true for all natural numbers n but for which the assumption that S(k) is true from some k is not needed to show that S(k+1) is true.

Any ideas?

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- Oct 18th 2010, 09:28 PMKatyCarInduction Statements
I'm trying to find an example of a statement S(n) that is true for all natural numbers n but for which the assumption that S(k) is true from some k is not needed to show that S(k+1) is true.

Any ideas? - Oct 19th 2010, 10:30 AMMoeBlee
I guess you mean: It is not required to show S(0) and to show S(k) implies S(k+1).

Let S be:

n = n