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, 20:59, 6 May 2008
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| ===Note 17=== | | ===Note 17=== |
| | | |
− | <pre>
| + | Any cell in a venn diagram has a well-defined set of nearest neighbors, and so we can apply a boundary operator of the appropriate rank to the list of signed features that conjoined would indicate the cell in view. |
− | Any cell in a venn diagram has a well-defined set of nearest neighbors, | |
− | and so we can apply a boundary operator of the appropriate rank to the | |
− | list of signed features that conjoined would indicate the cell in view. | |
| | | |
− | For example, having computed the "boundary", or what is more properly | + | For example, having computed the ''boundary'', or what is more properly called the ''point omitted neighborhood'' (PON) of the center cell in a 3-dimensional universe of discourse, what is the PON of the cell that is furthest from it, namely, the ''origin cell'' indicated by the proposition <math>(x)(y)(z)\!</math>? |
− | called the "point omitted neighborhood" (PON) of the center cell in a | |
− | 3-dimensional universe of discourse, what is the PON of the cell that | |
− | is furthest from it, namely, the "origin cell" indicated as (x)(y)(z)? | |
| | | |
− | The region bordering the origin cell, (x)(y)(z), can be computed by placing | + | The region bordering the origin cell, <math>(x)(y)(z),\!</math> can be computed by placing its three signed conjuncts in a 3-place bracket like <math>(\ldots,\ldots,\ldots),\!</math> arriving at the cactus expression that is shown in both graph and string forms below. |
− | its three signed conjuncts in a 3-place bracket like (__, __, __), arriving | |
− | at the cactus expression that is shown below in both graph and string forms. | |
| | | |
| + | <pre> |
| o-------------------------------------------------o | | o-------------------------------------------------o |
| | | | | | | |
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| | ((x),(y),(z)) | | | | ((x),(y),(z)) | |
| o-------------------------------------------------o | | o-------------------------------------------------o |
| + | </pre> |
| | | |
− | Figure 11 shows the venn diagram of this expression, | + | Figure 11 shows the venn diagram of this expression, whose meaning is adequately suggested by the phrase "just 1 of 3 is true". |
− | whose meaning is adequately suggested by the phrase | |
− | "just 1 of 3 is true". | |
| | | |
| + | <pre> |
| o-----------------------------------------------------------o | | o-----------------------------------------------------------o |
| | U | | | | U | |