(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assume B is a countable set. Thus, there exists [itex] f:\mathbb{N}→B [/itex]

which is 1-1 and onto Let [itex] A{\subseteq}B [/itex] be an infinte subset of B.

Show that A is countable.

3. The attempt at a solution

Lets assume for contradiction that A has an uncountable number of elements.

This would imply that A has elements that are not in B. But this is a contradiction because all elements in A are in B. Therefore A is countable.

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# Countable set Proof.

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