The multiplicative axiom is equivalent to the proposition that a product is only zero when at least one of its factors is zero; i.e. that, if any number of cardinal numbers be multiplied together, the result cannot be 0 unless one of the numbers concerned is 0.
The multiplicative axiom is equivalent to the proposition that, if
be any relation, and
any class contained in the converse domain of
, then there is at least one one-many relation implying
and having