Is the following a theorem from ZFC?(adsbygoogle = window.adsbygoogle || []).push({});

Given a collection C of non-empty sets that includes at least one infinite set, the cardinality of the collection of distinct choice functions on C (as defined in AC) equals the cardinality of the largest element of C.

My feeling that this is true is from generalizing the case when the largest cardinality is [itex]\aleph[/itex]_{0}, where it seems that a simple proof is possible, but I am not sure whether it is true and, if so, provable (from ZFC) for higher cardinalities.

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

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

# Number of choice functions?

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