Home page for accesible maths Math 101 Chapter 1: Sequences and Series 1.19 The sum of squares 1.21 Nonsense by induction

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1.20 Induction statements other than identities

In an induction proof, $P(n)$ can be a statement other than an equality, as the following example illustrates. Note the difference between ‘equals’ $(=)$ and ‘asserts that’ $(:)$ .

Example

To prove that $2^{n}>n\,$ holds for all positive integers $n\,$ .