Prove that if a and b are rational then a – b is rational.|If n = 4k + 3, does 8 divide n? – 1? Explain carefully.-

Introduction: In mathematics, a rational number is any number that can be represented in the form…

Answered: Prove that if a and b are rational then…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter7: Real And Complex Numbers

Section7.1: The Field Of Real Numbers

Problem 13E: Prove that is irrational. (That is, prove there is no rational number such that .)

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Similar questions

Prove that is irrational. (That is, prove there is no rational number such that .)
If x and y are positive rational numbers, prove that there exists a positive integer n such that nxy. This property is called the Archimedean Property of the rational numbers. (Hint: Write x=a/b and y=c/d with each of a,b,c,d+.)
13. Prove that if and are rational numbers such that then there exists a rational number such that . (This means that between any two distinct rational numbers there is another rational number.)
Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation can be proved to be true for n=k+1. Explain why this does not prove that the statement is true for all positive integers. Is the statement true for all positive integers? Why?
Prove that 23 is not a rational number.
Exercises Prove that the order of An is n!2.

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Prove that if a and b are rational then a – b is rationa If n = 4k+3 does 8 divide ² _ 1? Eplain carefully