Changes

==Charts and graphs==

==Charts and graphs==

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 represents each point of <math>\mathbb{B}^k</math> by the corresponding point of the <math>k\!</math>-cube.  The venn diagram picture represents each point of <math>\mathbb{B}^k</math> by the corresponding "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 corresponding point of the <math>k\!</math>-cube.  The venn diagram picture associates each point of <math>\mathbb{B}^k</math> with a corresponding "cell" of the venn diagram on <math>k\!</math> "circles".

In addition, each point of '''B'''^k is the unique point in the '''[[fiber (mathematics)|fiber]] of truth''' <math>[|s|]</math> of a '''singular proposition''' ''s''&nbsp;:&nbsp;'''B'''^''k''&nbsp;&rarr;&nbsp;'''B''', and thus it is the unique point where a '''singular conjunction''' of ''k'' '''literals''' is 1.

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 equal to 1.

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

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