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# 4. Induction - MATH 224 Discrete Mathematics Induction...

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8/27/09 11 MATH 224 – Discrete Mathematics Induction Induction allows us to prove properties that hold over the integers are some infinite subset of the integers. So for example it provides for a way to prove that X 3 – X is a multiple of 3 for all values of X ≥ 0. In this case, there is also a simple proof that doesn’t require induction. Induction can be illustrate by the problem of climbing a ladder. In order to climb a latter, you must be able to get to the first step and then from any step on the ladder to the next. The basis step requires that a property be true for the smallest value. Basis: Can you reach the first step? Yes Basis: Can you reach the first step?

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