Changes

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| align="right" width="36" | 2.

| align="right" width="36" | 2.

| <math>\Upsilon_p = \Upsilon (p, \_\_, \textstyle\prod) : (\mathbb{B}^k \to \mathbb{B}) \to \mathbb{B}.</math>

| <math>\Upsilon_p = \Upsilon (p, \underline{~~}, \textstyle\prod) : (\mathbb{B}^k \to \mathbb{B}) \to \mathbb{B}.</math>

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Throwing in the lower default value permits the following abbreviations:

Throwing in the lower default value permits the following abbreviations:

{|

{| celpadding="4"

| align=right width=36 | 3.

| align="right" width="36" | 3.

| &Upsilon;''q'' = &Upsilon;(''q'') = &Upsilon;₁ ''q'' = &Upsilon;(1, ''q'', &Pi;).

| <math>\Upsilon q = \Upsilon (q) = \Upsilon_1 q = \Upsilon (1, q, \textstyle\prod).</math>

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| align=right width=36 | 4.

| align="right" width="36" | 4.

| &Upsilon; = &Upsilon;(1, __, &Pi;) : ('''B'''^''k'' &rarr; '''B''') &rarr; '''B'''.

| <math>\Upsilon = \Upsilon (1, \underline{~~}, \textstyle\prod)) : (\mathbb{B}^k\ \to \mathbb{B}) \to \mathbb{B}.</math>

|}<br>

|}<br>

This means that &Upsilon;''q'' = 1 if and only if ''q'' holds for the whole universe of discourse in question, that is, if and only ''q'' is the constantly true proposition '''1''' : '''B'''^''k'' &rarr; '''B'''. The ambiguities of this usage are not a problem so long as we distinguish the context of definition from the context of application and restrict all shorthand notations to the latter.

This means that <math>\Upsilon q = 1\!</math> if and only if <math>q\!</math> holds for the whole universe of discourse in question, that is, if and only <math>q\!</math> is the constantly true proposition <math>1 : \mathbb{B}^k \to \mathbb{B}.</math>  The ambiguities of this usage are not a problem so long as we distinguish the context of definition from the context of application and restrict all shorthand notations to the latter.

===Measure for Measure===

===Measure for Measure===