assignment9-answers

# This definition says that for all n n that for that

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Unformatted text preview: n = 150 and m = 45. Then 150 = 3*45 + 15 45 = 3*15 + 0 15 is the gcd of 150 and 45. Example 2. Let n = 3744 and m = 390. Then 3744 = 9*390 + 234 390 = 1*234 + 156 234 = 1 * 156 + 78 156 = 2*78 + 0 So 78 is the gcd. In fact 3744 = 48*78 and 390 = 5*178. Problem 9 5: Any function X from N to R defines a sequence of real numbers, X1, X2, … The number A is defined to be the limit of Xn as n → ∞ if this is true: For every ε > 0, there is a positive integer N so that for all n > N, | Xn – A| < ε. Notation: limn → ∞ X n = A € Comment: It is not necessary to assume N is an integer, since if we have any non ­ integer N with this property, then the integer N' obtained by rounding up N to an € integer in the segment [N, N+1] will...
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