(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Countable set Proof.

**Physics Forums | Science Articles, Homework Help, Discussion**