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Unformatted text preview: a Øh4Ô Ö iÒg6ÓÑ eÛ Ó Ök# 4 Ó ÐÙ Ø iÓÒ ×bÝ iÑC a ÐÐahaÒ § 1.8 Problem 2 ( a ): This is not a function. If the input is n = 1 then the output is ± 1, which is two different values. ( b ): This is a function. For every integer n the value of √ n 2 + 1 is a single welldefined real number. ( c ): This is not a function from all of Z to R . Note that if n = 2 or n = − 2 then f ( n ) is undefined. § 1.8 Problem 8 ( a ): ⌊ 1 . 1 ⌋ = 1. ( b ): ⌈ 1 . 1 ⌉ = 2. ( c ): ⌊− . 1 ⌋ = − 1. ( d ): ⌈− . 1 ⌉ = 0. ( e ): ⌈ 2 . 99 ⌉ = 3. ( f ): ⌈− 2 . 99 ⌉ = − 2. ( g ): ⌊ 1 2 + ⌈ 1 2 ⌉⌋ = ⌊ 1 2 + 1 ⌋ = ⌊ 3 2 ⌋ = 1. ( h ): ⌈⌊ 1 2 ⌋ + ⌈ 1 2 ⌉ + 1 2 ⌉ = ⌈ 0 + 1 + 1 2 ⌉ = ⌈ 3 2 ⌉ = 2. § 1.8 Problem 12 ( a ): f ( n ) = n − 1 is onetoone, because if n negationslash = m then n − 1 negationslash = m − 1, and so f ( n ) negationslash = f ( m ). Thus different inputs produce different outputs....
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 Spring '06
 CALLAHAN
 Integers

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