Problem 3. For real numbers x, we defined [z] as the unique integer such that[x] ≤ x < [x] +1.Prove the following properties:(a) [x + n] = [x] +n for every integer n.(b) [x+y] is equal to [x] + [y] or [x] + [y] + 1.(c) [2x] = [x] + [x]

Let, x be a real number. Then the greatest integer function [x] as the unique integer, is defined as…

Problem 3. For real numbers x, we defined [z] as the unique integer such that [2] ≤ x < [x] +1. Prove the following properties: (a) [r+ n] = [x] +n for every integer n. (b) [r+y] is equal to [x] + [y] or [x] + [y] + 1. (c) [2x] = [x] + [+]

Problem 3. For real numbers x, we defined [z] as the unique integer such that [2] ≤ x < [x] +1. Prove the following properties: (a) [r+ n] = [x] +n for every integer n. (b) [r+y] is equal to [x] + [y] or [x] + [y] + 1. (c) [2x] = [x] + [+]

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 51E

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Question

Problem 3. For real numbers x, we defined [z] as the unique integer such that
[x] ≤ x < [x] +1.
Prove the following properties:
(a) [x + n] = [x] +n for every integer n.
(b) [x+y] is equal to [x] + [y] or [x] + [y] + 1.
(c) [2x] = [x] + [x]

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