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April 09, 2015, 07:56:11 PM |
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This is from the last homework assignment.. the more recent one I think is involving infinite sets more.. I should have the latest one in a few hours, but right now I'm simply looking to see if this gets any attention.
Let f : X = Z × {0} → Y = Z × {1} be the map f(n, 0) = (2n + 1, 1) and g : Y = Z × {1} → X = Z × {0} the map g(n, 1) = (2n − 2, 0). (i) Which elements of X have exactly one predecessor? (i.e. x ∈ im g but g −1 (x) ∈/ im f). Which elements of X are the endpoints of chains of length 2 but not of longer chains? Which of Xe, Xo and Xi does (0, 0) belong to ? (ii) Which set does the element (2nk, 0) belong to, where k is odd and n ≥ 0?
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