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Example

We prove that every natural number greater than 1 can be factorized into a sequence of prime numbers, i.e.,

forall n in N: n > 1 =>
   (exists k in N, f: Nk -> N: n = (prod0 <= i < k f(i)) /\  forall i in Nk: f(i) is prime).
We proceed by complete induction over n.

We take arbitrary n in N and assume

(1) forall m < n: m > 1 =>
   (exists k in N, f: Nk -> N: m = (prod0 <= i < k f(i)) /\  forall i in Nk: f(i) is prime).
We have to show
n > 1 =>
   (exists k in N, f: Nk -> N: n = (prod0 <= i < k f(i)) /\  forall i in Nk: f(i) is prime).

See lecture notes.


Author: Wolfgang Schreiner
Last Modification: November 24, 1999

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