How can I send VALENTINES? ---

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How can I send VALENTINES? --- Let me count the
ways.
SUBSETS
OF MY SET OF FRIENDS
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, ,
S
the POWER SET of S

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2 x 2 x 2
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If a set S has n members, then S has
2n subsets. ie the POWER SET of S has 2n
members
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When S is a finite set, the power set of S
contains more members Than S .. A finite
set has more subsets than members.
Cantor proved the same for infinite sets ie
for any set S, The power set of S has a greater
cardinal number than S.
We will examine the infinite set N 1, 2, 3,
4, 5, and the power set of N
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If there is a one to one correspondence
between N and P(N) it would look like
this
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(No Transcript)
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2 is NOT a member of S2
3 is NOT a member of S3
5 is NOT a member of S5
7 is NOT a member of S7
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2 is NOT a member of S2
3 is NOT a member of S3
5 is NOT a member of S5
7 is NOT a member of S7
Build a set containing all the numbers that do
NOT belong to their paired set
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2 is NOT a member of S2
3 is NOT a member of S3
5 is NOT a member of S5
7 is NOT a member of S7
Build a set containing all the numbers that do
NOT belong to their paired set call this set Sk
and include it in the list of subsets it must
correspond to some natural number k.
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Is k a member of Sk ?
If it is then it isnt. If it isnt then it is.
m / m is NOT a member of Sm