Re: Assume that S=(a),

In article <u9lt23l6c7gibtu06hmsnj7ndq17fo05ev@xxxxxxx>,
quasi <quasi@xxxxxxxx> wrote:
On 24 Apr 2007 18:57:07 -0700, cyberbloke <cyberbloke@xxxxxxxxx>
wrote:

Assume that S=(a), What is 2 raised to the power of S equal to?

{{a}} or (a) or {emptyset{a}}

Perhaps you meant S={a}.

If so, 2^S is just the set of all subsets of S.

To be more precise, if A and B are sets, then A^B is the set of all
functions from B to A. If we take 2 to be the set {0,1}, then 2^S is
thus the set of all functions from S to {0,1}.

This set happens to be the set of all "characteristic functions" of S,
which has a canonical one-to-one correspondence with the set of all
subsets of S; but 2^S is not the power set of S, exactly.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

.

Relevant Pages