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. | 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. |