Mathematics, 08.10.2019 00:00 goblebrandon

Prove or disprove each of the se 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 ⌋≤⌊ 2 x ⌋ + ⌊ 2 y ⌋ for all realnumbers x and y

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Prove or disprove each of the se statements about the ﬂoor and ceiling functions. a) ⌊⌈ x ⌉⌋ = ⌈ x ⌉...

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