real numbers such that a < b.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
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Suppose that a and b are distinct real numbers such that a < b.
a) Prove that the set {x eR : a < x < b} is uncountable.
b) Prove that the set {x e Q : a < x < b} is countably infinite.
Transcribed Image Text:Suppose that a and b are distinct real numbers such that a < b. a) Prove that the set {x eR : a < x < b} is uncountable. b) Prove that the set {x e Q : a < x < b} is countably infinite.
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