Unformatted text preview: number deﬁned by this Cauchy sequence is denoted 0 .e 1 e 2 e 3 ... ) (b) Show that 0 . 999 ... = 1. (3) Section 2.2.4 #5. (4) Using the triangle inequality, show that for any a,b ∈ R , we have  a    b  ≤  ab  . Using this, show that if { x n } is a sequence of real numbers which converges to L , then { x n } converges to  L  . 1...
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 '08
 PROTSAK
 Metric space, Rational number, Limit of a sequence, Cauchy sequence

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