It is very instructive to examine the matrix representation of <math>\mathit{l}^\mathrm{w}\!</math> at this point, not the least because it dispels the mystery of the name ''involution''.
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It is very instructive to examine the matrix representation of <math>\mathit{l}^\mathrm{w}\!</math> at this point, not the least because it effectively dispels the mystery of the name ''involution''. First, let us make the following observation. To say that <math>\mathrm{J}\!</math> is a lover of every woman is to say that <math>\mathrm{J}\!</math> loves <math>\mathrm{K}\!</math> if <math>\mathrm{K}\!</math> is a woman. This can be rendered in symbols as follows:
To say that <math>\mathrm{J}\!</math> is a lover of every woman is to say that <math>\mathrm{J}\!</math> loves <math>\mathrm{K}\!</math> if <math>\mathrm{K}\!</math> is a woman. This can be rendered in symbols as follows: