CSCA67H3 Lecture Notes - Natural Number, Elementary Arithmetic, Prime Number

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17 Apr 2011
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CSCA67H3 Full Course Notes
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CSCA67H3 Full Course Notes
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A proof is a convincing argument that a statement is true: what makes up a proof, a set of basic statements that we agree are true for a spec- i ed domain. E. g. , if d = r then we have the basic rules about arithmetic and inequalities: a series of logical steps that build on previously proven statements. We are concerned with the content of a proof and the structure of the proof. Why do we believe this claim: if x 2 then x + 2 2 + 2 = 4 by arithmetic, squaring both sides, gives (x + 2)2 16. There exists an integer x such that x2 + 6x + 9 = 0. There does not exist a largest natural number. Why do we believe this claim: pick any arbitrary natural number x, we know by basic arithmetic, that x + 1 is a natural number and larger than x.

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