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a. Show that if a, b, c, de Zwith a +b√2 = c+d√2, then a = c and b=d. You may use, without proof, the fact that √2 Q. b. Let W = {a+b√2 a, b = Z}. Is W countable? Explain why or why not. You may use the result in part (a). -

a. Show that if a, b, c, de Zwith a +b√2 = c+d√2, then a = c and b=d. You may use, without proof, the fact that √2 Q. b. Let W = {a+b√2 a, b = Z}. Is W countable? Explain why or why not. You may use the result in part (a). -

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 50E: 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...
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Q6/ a. Show that if a, b, c, d € Z with a +b√2 = c+d√2, then a = c and b = d. You may use, without proof, the fact that √2 Q. b. Let W = {a+b√2 | a, b € Z}. Is W countable? Explain why or why not. You may use the result in part (a). -
Transcribed Image Text:Q6/ a. Show that if a, b, c, d € Z with a +b√2 = c+d√2, then a = c and b = d. You may use, without proof, the fact that √2 Q. b. Let W = {a+b√2 | a, b € Z}. Is W countable? Explain why or why not. You may use the result in part (a). -
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