MATH 241 Lecture 6: Proofs by Contradiction and by Cases
28 Jan 2019
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Lecture 6:proof by contradiction Sby cases
Document Summary
S by cases provisionality we have to show that if h in hz ^ hk is true , then. C and show a contradiction ( p n. C is false so c is true example 1) there are infinitely many prime numbers proof : suppose , to the contrary , there are finitely many prime number we "ll call them. , pk so it must not be prime . there is a prime number pj which divides it . since pj in and pjl pi. I but no prime number divides one so there"s a contradiction we conclude our statement was false. S there are infinitely many prime numbers dx example 2) prove that the product of a nonzero rational number. S an irrational number is rational proof : suppose , to the contrary , that the product is rational. Thus fx = ed where a , b. , c , d e z and x is irrational.
