- by Brad Bart, Simon Fraser University Summary Summary Mathematical induction is a tool to prove, i.e., to make arguments about, mathematical structures which are self-similar. In the simplest case, the structure can be stated using a single parameter n, where n spans the positive integers: 1, 2, 3, 4, . . . . For example, suppose you are interested in the sum of the first n odd integers. That is, 1, 1 + 3, 1 + 3 + 5, 1 + 3 + 5 + 7, . . . and you discover a pattern: 1 = 1 16 = 1 + 3 + 5 + 7 So, you make a guess! . . . a claim!
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