Changes

Two ways of visualizing the space <math>\mathbb{B}^k</math> of <math>2^k\!</math> points are the [[hypercube]] picture and the [[venn diagram]] picture.  The hypercube picture associates each point of <math>\mathbb{B}^k</math> with a unique point of the <math>k\!</math>-dimensional hypercube.  The venn diagram picture associates each point of <math>\mathbb{B}^k</math> with a unique "cell" of the venn diagram on <math>k\!</math> "circles".

Two ways of visualizing the space <math>\mathbb{B}^k</math> of <math>2^k\!</math> points are the [[hypercube]] picture and the [[venn diagram]] picture.  The hypercube picture associates each point of <math>\mathbb{B}^k</math> with a unique point of the <math>k\!</math>-dimensional hypercube.  The venn diagram picture associates each point of <math>\mathbb{B}^k</math> with a unique "cell" of the venn diagram on <math>k\!</math> "circles".

In addition, each point of <math>\mathbb{B}^k</math> is the unique point in the '''[[fiber (mathematics)|fiber]] of truth''' <math>[|s|]\!</math> of a '''singular proposition''' <math>s : \mathbb{B}^k \to \mathbb{B},</math> and thus it is the unique point where a '''singular conjunction''' of <math>k\!</math> '''literals''' is <math>1.\!</math>

In addition, each point of <math>\mathbb{B}^k</math> is the unique point in the ''[[fiber (mathematics)|fiber]] of truth'' <math>[|s|]\!</math> of a ''singular proposition'' <math>s : \mathbb{B}^k \to \mathbb{B},</math> and thus it is the unique point where a ''singular conjunction'' of <math>k\!</math> ''literals'' is <math>1.\!</math>

For example, consider two cases at opposite vertices of the cube:

For example, consider two cases at opposite vertices of the cube: