Q2 Let C = {r : x e Z}. (a) Show that C'nQ+ 0. (le. show C contains a rational.) (b) Prove that CnR\Q#0. (le. show C contains an irrational.) (c) Prove C is countable. (d) Is R\ C countable or uncountable? Justify your answer.
Q2 Let C = {r : x e Z}. (a) Show that C'nQ+ 0. (le. show C contains a rational.) (b) Prove that CnR\Q#0. (le. show C contains an irrational.) (c) Prove C is countable. (d) Is R\ C countable or uncountable? Justify your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Q2
Let C = {x : r E Z}.
(a) Show that CnQ + 0. (le. show C contains a rational.)
(b) Prove that CnR\Q#0. (le. show C contains an irrational.)
(c) Prove C is countable.
(d) Is R \ C countable or uncountable? Justify your answer.
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