@EliahKagan Similarly,
{0, 1} = {1, 0}
(due to the
axiom of extensionality, i.e., sets are equal just when they have the same elements), but you might be surprised at the prevalence of the view that this shows
=
doesn't really mean "is the same as", because the second symbol (or, if you prefer, first-listed element) in
{0, 1}
is a
0
but the second symbol (or, if you prefer, first listed element) in
{1, 0}
is a
1
.