|—||L. J. J. W.|
|—||Tim Williamson, Knowledge and its Limits.|
|—||Francis Bacon (thanks @jessicajthames)|
with members of the power set of A that assigns to each distinct
member of A a distinct subset of A. Let S be the set of all members
of A that are not members of the subset assigned to them. S is a
a subset of A. But S is not assigned to any member of A. For suppose
it were assigned to a member, say x, of A. Then x would be a member
of S if and only if it were not a member of S. This is a contradiction.
So any pairing-off of distinct members of A with distinct members
of the power set of A leaves some member of the power set unpaired.
So there is no 1-1 correspondence between A and its power set.
|—||Cantor’s Theorem as explained by Geoffrey Hunter (Metalogic, p. 24)|
1- I want to know everything.
2- I want to know everything about something.
3- I want to know something about something.
4- I want tenure.
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