Sets: Cardinality and FunctionsDate: 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/ |
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