Re: Power Set and Collection of finites subsets of N

iAGENT wrote (in part):

Power Set is collection of all subsets of N.
Can anybody tell me how Power Set is different
from collection of finite subsets of N?

Resolving this issue will probably clear up the
other thing you asked about. The following are
subsets of N, but not finite subsets of N:

{2, 4, 6, 8, ...}

{3, 6, 9, 12, ...}

{2, 2^2, 2^3, 2^4, ...}

{n: n is a prime number}

You're overlooking the infinite subsets of N.
Indeed, "almost all" subsets of N are infinite. The
collection of infinite subsets of N as compared to
the collection of finite subsets of N is somewhat
like the collection of finite subsets of N as
compared to the collection of empty subsets of N
(the latter is a collection that contains only
one set).

Dave L. Renfro

.

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