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Mathematics, 23.10.2020 06:01 SapphireWolf
Prove or disprove each of these statements about the floor and ceiling functions. a) ⌊⌈x⌉⌋ = ⌈x⌉ for all real numbers x. b) ⌊x+y⌋=⌊x⌋+⌊y⌋for all real numbers x and y. c) ⌈⌈x∕2⌉ ∕2⌉ = ⌈x∕4⌉ for all real numbers x. d)⌊√⌈x⌉⌋ = ⌊√x ⌋ for all positive real numbers x. e) ⌊x⌋+⌊y⌋+⌊x+y⌋≤⌊2x⌋+⌊2y⌋forall real numbers x and y.
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Prove or disprove each of these statements about the floor and ceiling functions. a) ⌊⌈x⌉⌋ = ⌈x⌉ for...
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