Let x be a real number. Prove that x is an integer if and only if [0.891a] + [0.109æ] =

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.2: Solving Inequalities
Problem 65WE
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Let x be a real number. Prove that
x is an integer
if and only if
[0.891a] + [0.109x] = x .
Be sure to set out your argument clearly and logically. Carelessly written proofs will not receive good marks.
Syntax advice: You can use floor (x) and ceil (x) for |x] and [x] respectively. Also, remember not to use <
followed immediately by a letter.
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Transcribed Image Text:Let x be a real number. Prove that x is an integer if and only if [0.891a] + [0.109x] = x . Be sure to set out your argument clearly and logically. Carelessly written proofs will not receive good marks. Syntax advice: You can use floor (x) and ceil (x) for |x] and [x] respectively. Also, remember not to use < followed immediately by a letter. IT Equation Q Editor A- A- I BIUS X x Styles Font Size
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