Unformatted text preview: A is bounded above”; (b) “the set A is not bounded above”; (c) a = sup A . 2. Longer Questions B1. Let f : X → Y be a function. (a) State the deﬁnitions of “ f is an injection” and “ f is a surjection”. (b) Prove that if f is a bijection then f is invertible. (c) Prove that the function f : R {2 } → R {1 } , f ( x ) = 3x x + 2 is a bijection and ﬁnd its inverse. B2. (a) State and prove the Archimedian Principle. (You may use without proof the theorem on existence of the supremum for a set of real numbers which is bounded above.) (b) Let A = ± 3 n6 n  n ∈ N + ² . Find the supremum of the set A ? Justify your answer using the Archimedian Principle. 1...
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 Fall '08
 IvorMcGillivray
 Archimedian, separate answer book, longer questions

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