5. Suppose A, B are countably infinite sets, meaning that there exists one-to-one corre- spondences f : N → A and g : N → B. Prove that A x B is also countably infinite.
5. Suppose A, B are countably infinite sets, meaning that there exists one-to-one corre- spondences f : N → A and g : N → B. Prove that A x B is also countably infinite.
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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Hint: Use that N × N is countably infinite,
Transcribed Image Text:5. Suppose A, B are countably infinite sets, meaning that there exists one-to-one corre-
spondences f : N → A and g : N → B. Prove that A x B is also countably infinite.
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