Equivalent to Tychonoff's Theorem, which states that any product of compact topological spaces is compact.  It is also equivalent to the statement that any vector space over a field has a basis over that field.  Cohen and G?del showed that neither accepting it nor rejecting it leads to a contradiction.   And Russell likened it to the ability to decide if a sock is left-footed or right-footed.  FTP, name this mathematical assertion that is normally stated: for any collection of nonempty sets, we can choose a member from each set in that collection.
Equivalent to Tychonoff's Theorem, which states that any product of compact topological spaces is compact.  It is also equivalent to the statement that any vector space over a field has a basis over that field.  Cohen and G?del showed that neither accepting it nor rejecting it leads to a contradiction.   And Russell likened it to the ability to decide if a sock is left-footed or right-footed.  FTP, name this mathematical assertion that is normally stated: for any collection of nonempty sets, we can choose a member from each set in that collection.
Equivalent to Tychonoff's Theorem, which states that any product of compact topological spaces is compact.  
axiom of choice (accept Zorn's lemma or well ordering theorem)