# L05_proofs_by_contradiction - 1-1Proof by Smallest...

This preview shows pages 1–6. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1-1Proof by Smallest CounterexampleDefinitions:•log2(n)isxsuch that2x=n.blog2(n)cis the uniqueis.t.2i≤n <2i+1e.g.blog2(2)c= 1,blog2(3)c= 1,blog2(4)c= 2blog2(31)c= 4,blog2(32)c= 5,blog2(33)c= 51-2Proof by Smallest CounterexampleDefinitions:•log2(n)isxsuch that2x=n.blog2(n)cis the uniqueis.t.2i≤n <2i+1•Prime factorization ofnis the representation ofnasmultiplication of a list of primes.e.g.12 = 2×2×3,6! = 2×2×2×2×3×3×5e.g.blog2(2)c= 1,blog2(3)c= 1,blog2(4)c= 2blog2(31)c= 4,blog2(32)c= 5,blog2(33)c= 51-3Proof by Smallest CounterexampleDefinitions:•log2(n)isxsuch that2x=n.blog2(n)cis the uniqueis.t.2i≤n <2i+1•Prime factorization ofnis the representation ofnasmultiplication of a list of primes.e.g.12 = 2×2×3,6! = 2×2×2×2×3×3×5•DefineSIZE(n)to be thenumber of prime factorsinprime factorization ofn.e.g.SIZE(12) = 3,SIZE(6!) =SIZE(720) = 7e.g.blog2(2)c= 1,blog2(3)c= 1,blog2(4)c= 2blog2(31)c= 4,blog2(32)c= 5,blog2(33)c= 52-1Proof by Smallest CounterexampleTheorem:For any positive integern,SIZE(n)≤ blog2(n)c.2-2Proof by Smallest CounterexampleTheorem:For any positive integern,SIZE(n)≤ blog2(n)c....
View Full Document

{[ snackBarMessage ]}