47

45

of different B's to the same A for every A to
reduce its converse to a one-to-one relation of every A
to a B. Thus we have proved that if there is no
one to one relation of every B to some A there is a one to one
relation of every A to some B. [go to p 60]

[skip] Let us now look into another problem.
Dr. Georg Cantor has a wonderful system
of Ordinal Numbers which I must explain to you.
It begins with the ordinary ordinal numbers
1, 2, 3 4 5 6 7 8 9 10 11 ...
That series is endless. That is to say, it has no
last. But neither in logic nor in fact does that
interfere with its being gone completely through provided
the objects numbered are not in the nature of existences.
When for instance Achilles runs after

45

of different B's to the same A for every A to
reduce its converse to a one-to-one relation of every A
to a B. Thus we have proved that if there is no
one to one relation of every B to some A there is a one to one
relation of every A to some B. [go to p 60]

[skip] Let us now look into another problem.
Dr. Georg Cantor has a wonderful system
of Ordinal Numbers which I must explain to you.
It begins with the ordinary ordinal numbers
1, 2, 3 4 5 6 7 8 9 10 11 ...
That series is endless. That is to say, it has no
last. But neither in logic nor in fact does that
interfere with its being gone completely through provided
the objects numbered are not in the nature of existences.
When for instance Achilles runs after