I would not have thought that "( $an_undefined_variable == 0 )" would evaluate to true because, golly, undef isn't a number and so the "==" operator is testing whether one number is the same as another number.

The "==" operator is comparing the left hand side and the right hand side in numeric context.
And, in numeric context, undef and 0 are equivalent:

C:\>perl -e "print 'ok' if undef == 0;"
ok
C:\>
[download]

But in string context, it's a different matter:

C:\>perl -e "print 'ok' if undef eq 0;"

C:\>
[download]

Cheers,
Rob