So Munkres, on page 424 of Topology (2nd edition) says that "...two free groups are isomorphic if and only if their systems of free generators have the same cardinality (We have proved these facts in the case of finite cardinality)."(adsbygoogle = window.adsbygoogle || []).push({});

Nowhere explicitly does he say this, although it seems that many of the theroems and corollaries allude to it. I've tried a few different things to see a proof that applies only in the finite case, but I'm not sure I have it right.

Any help would be much appreciated.

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# Finitely Generated Free Groups

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