Sets: Cardinality and Functions

Date: 06/29/98 at 03:34:36
From: Barbierato Marco
Subject: Sets

What does "{1,0}^{a,b}" mean? I'm looking for all kinds of 
information.

Thanks a lot.

Marco Barbierato

Date: 06/29/98 at 07:53:53
From: Doctor Jerry
Subject: Re: Sets

Hi Marco,

If A and B are sets, then A^B is the cardinal number of the set of all 
functions defined on B and taking their values in A.

So, if A={1,0} and B={a,b}, A^B has the cardinality of the set of 
functions

f(a)=0, f(b)=0,
g(a)=0, g(b)=1,
h(a)=1, h(b)=0,
k(a)=1, k(b)=1.

There are four functions from B to A (2^2).

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/