Sunday, December 25, 2016

abstract algebra - Powerset bijection problem

Please do not provide a full answer for this.



Let 2S={f:S{0,1}}. For AS, define χA2S by
χA(s)={0if sA1if sA.
Show that μ:P(S)2S given by μ(A)=χA is a bijection.



I know that the standard procedure for showing that a function is bijective is to show that it is both injective and surjective, and the "standard procedures" for those as well. It's just that I don't really know where to start with this.

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