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# 03_Slides - Definitions Using Previous Knowledge...

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Definitions Using Previous Knowledge Mathematical Terminology Summary Reading, Writing and Discovering Proofs Steven Furino Part 3: Definitions and Mathematical Terminology c 2011 Steven Furino Steven Furino Reading, Writing and Discovering Proofs

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Definitions Using Previous Knowledge Mathematical Terminology Summary Definition A definition in mathematics is an agreement, by all parties concerned, as to the exact meaning of a particular term. I An integer n divides an integer m , and we write n | m , if there exists an integer k so that m = kn . I An integer p > 1 is prime if the only positive integers that divide p are 1 and p . I A triangle is isosceles if two of its sides are equal in length. I An integer n is even if and only if the remainder when n is divided by 2 is 0. I Two statements A and B are equivalent if and only if “ A implies B ” and “ B implies A .” I The statement “ A AND B ,” written A B , is true if and only if A is true and B is true. I The statement “ A OR B ,” written A B , is true in all cases except where A is false and B is false. Steven Furino Reading, Writing and Discovering Proofs
Definitions Using Previous Knowledge Mathematical Terminology Summary Using Definitions in Proofs I Answering key questions in the backwards process. I Deriving new statements in the forward process. Steven Furino Reading, Writing and Discovering Proofs

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Definitions Using Previous Knowledge Mathematical Terminology Summary Equivalent Statements The following two statements are equivalent but only the first one is a definition. A: An integer n is even if and only if the remainder when n is divided by 2 is 0. B: An integer n is even if and only if there exists an integer k so that n = 2 k . Expressions that indicate equivalence: I A is equivalent to B I A is true if and only if B is true I A if and only if B I A iff B I A is necessary and sufficient for B I A B Steven Furino Reading, Writing and Discovering Proofs
Definitions Using Previous Knowledge

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03_Slides - Definitions Using Previous Knowledge...

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