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We have n2 = O(2n):

Proof: We assume not n2 = O(2n) and show a contradiction. By assumption, we have ~exists c in R, m in N: forall n >= m: |n2| <= c|2n|, i.e.,

forall c in R, m in N: ~forall n >= m: |n2| <= c|2n|.

We prove

forall n >= 0: n2 <= 2*2n
by induction on n and thus have a contradiction.

See lecture notes.

Author: Wolfgang Schreiner
Last Modification: December 14, 1999

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