Theorems

Theorems - CSE 1400 Applied Discrete Mathematics Theorems...

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CSE 1400 Applied Discrete Mathematics Theorems Department of Computer Sciences College of Engineering Florida Tech Spring 2011 1 Theorems 1 1 . 1 Theorems about Arithmetic 1 1 . 2 Theorems about Algebra 2 1 . 3 Theorems about Sets 2 1 . 4 Theorems about Boolean Logic 3 1 . 5 Theorems about Predicate Logic 3 1 . 6 Theorems about Relations 3 1 . 7 Theorems about Functions 3 1 . 8 Theorems about Sequences 4 1 . 9 Theorems about Modular Numbers 4 1 . 10 Theorems about Theorems 4 1 Theorems Abstract Theorems are statements that have been proven True . 1 . 1 Theorems about Arithmetic Theorem 1 (Fundamental Theorem of Arithmetic) . Every natural number m greater than 1 is either prime or the product of unique prime factors. The order of the prime factors is not considered important. Theorem 2 (Well-Ordering) . Let X be a non- empty subset of the natural numbers . There exists an element a X such that a x for all x X . This element a is called the least element of X . Theorem 3 (Archimedean property) . For every natural number m there is a natural number n such that n > m.
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cse 1400 applied discrete mathematics theorems 2 Theorem 4 (Quotient-Remainder) . Given an integer a Z and an integer n 6 = 0 , there exists an integer q and a natural number r, called the quotient and remainder, such that a = q · n + r and 0 r < | n | . Theorem 5 (Euclid’s Theorem) . There is no largest prime number. Lemma 1 . If a 2 is an even integer, then a is even. Theorem
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Theorems - CSE 1400 Applied Discrete Mathematics Theorems...

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