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If <math>L\!</math> is visualized as a solid body in the 3-dimensional space <math>X \times Y \times Z,\!</math> then <math>\operatorname{Proj}^{(2)}(L)\!</math> can be visualized as the arrangement or ordered collection of shadows it throws on the <math>XY,\!</math> <math>XZ,\!</math> and <math>YZ\!</math> planes, respectively.

If R is visualized as a solid body in the 3 dimensional space XxYxZ, then Proj (R) can be visualized as the arrangement or ordered collection of shadows it throws on the XY, XZ, and YZ planes, respectively.

There are a couple of set theoretic constructions that are useful here, in particular for describing the source and target domains of Proj.

A couple of set-theoretic constructions are useful here, in particular for describing the source and target domains of the projection operator <math>\operatorname{Proj}^{(2)}.\!</math>

1. The set of subsets of a set S is called the "power set" of S.  This object is denoted by either of the forms "Pow (S)" or "2S" and defined as follows:

1. The set of subsets of a set S is called the "power set" of S.  This object is denoted by either of the forms "Pow (S)" or "2S" and defined as follows: