Let A be an infinite set. Show that there exists a proper subset B of A such that |A| = |B|. Does your proof use the Axiom of Choice?

Asked Apr 09 '20 at 17:57

Active Apr 09 '20 at 17:59

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Any ideas on how to prove this?

edited Apr 09 '20 at 17:59

mrtaurho

asked Apr 09 '20 at 17:57

user770210

1

How are you defining infinite set? Because this is one possible definition of it. Also, what have you tried? – Rushabh Mehta Apr 09 '20 at 17:58
Hint: Pick any $x\in A$. Is $A \setminus {x}$ infinite? – J. De Ro Apr 09 '20 at 18:03

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