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the Bs which this would require do not exist. Add other
things, say Cs to the Bs and every A would
be provided with its own particular separate B or C. Take no
more Cs than are required, and conversely every
B or C would have its own separate A and
therefore every B has its own separate A.

Hence we get the proposition if the collection of As is not as small
as the collection of Bs then the collection of Bs
must be as small as the collection of As.

This proposition has been a great puzzle to
the mathematicians. They have endeavored in
vain to prove it. The truth is that it never can be
mathematically proved because it depends upon the
peculiar nature of relations which is a question
of logic, not of mathematics. Hence, every proposed