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arises the question, why may not two
collections each be greater than the other?
To this an obvious reply is that if
nothing at all be considered as a collection,
as a mathematician would naturally
consider it, that collection is greater than
itself. Now if that be possible, the idea of magnitude
breaks down. There are logico-mathematicians
who think it is possible.

But there are others, Cantor among them,
who think not. To me the notion that
every one-to-one relation between As
and Bs should leave over some As unrelated
to any Bs although there are B to which
no As are related, and that there should
be no relation whatever in which these
unoccupied As could stand to those unoccupied
Bs is contrary to the nature

arises the question, why may not two
collections each be greater than the other?
To this an obvious reply is that if
nothing at all be considered as a collection,
as a mathematician would naturally
consider it, that collection is greater than
itself. Now if that be possible, the idea of magnitude
breaks down. There are logico-mathematicians
who think it is possible.

But there are others, Cantor among them,
who think not. To me the notion that
every one-to-one relation between As
and Bs should leave over some As unrelated
to any Bs although there are B to which
no As are related, and that there should
be no relation whatever in which these
unoccupied As could stand to those unoccupied
Bs is contrary to the nature