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To set the 2-adic relative term <math>~v~</math> within a suitable context of interpretation, let us suppose that <math>~v~</math> corresponds to a relation <math>V \subseteq R \times S,</math> where <math>~R~</math> is the set of real numbers and <math>~S~</math> is a suitable syntactic domain, here described as "terms".  Then the 2-adic relation <math>~V~</math> is evidently a function from <math>~S~</math> to <math>~R.~</math>  We might think to use the plain letter <math>{}^{\backprime\backprime} v {}^{\prime\prime}</math> to denote this function, as <math>v : S \to R,</math> but I worry this may be a chaos waiting to happen.  Also, I think we should anticipate the very great likelihood that we cannot always assign numbers to every term in whatever syntactic domain <math>~S~</math> that we choose, so it is probably better to account the 2-adic relation <math>~V~</math> as a partial function from <math>~S~</math> to <math>~R.~</math>  All things considered, then, let me try out the following impedimentaria of strategies and compromises.

To set the 2-adic relative term <math>~v~</math> within a suitable context of interpretation, let us suppose that <math>~v~</math> corresponds to a relation <math>V \subseteq \mathbb{R} \times S,</math> where <math>\mathbb{R}</math> is the set of real numbers and <math>~S~</math> is a suitable syntactic domain, here described as "terms".  Then the 2-adic relation <math>~V~</math> is evidently a function from <math>~S~</math> to <math>\mathbb{R}.</math>  We might think to use the plain letter <math>{}^{\backprime\backprime} v {}^{\prime\prime}</math> to denote this function, as <math>v : S \to \mathbb{R},</math> but I worry this may be a chaos waiting to happen.  Also, I think we should anticipate the very great likelihood that we cannot always assign numbers to every term in whatever syntactic domain <math>~S~</math> that we choose, so it is probably better to account the 2-adic relation <math>~V~</math> as a partial function from <math>~S~</math> to <math>\mathbb{R}.</math>  All things considered, then, let me try out the following impedimentaria of strategies and compromises.

First, I adapt the functional arrow notation so that it allows us to detach the functional orientation from the order in which the names of domains are written on the page.  Second, I change the notation for ''partial functions'', or ''pre-functions'', to one that is less likely to be confounded.  This gives the scheme:

First, I adapt the functional arrow notation so that it allows us to detach the functional orientation from the order in which the names of domains are written on the page.  Second, I change the notation for ''partial functions'', or ''pre-functions'', to one that is less likely to be confounded.  This gives the scheme:

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For now, I will pretend that ''v'' is a function in ''R'' of ''S'', ''v'' : ''R'' &larr; ''S'', amounting to the functional alias of the 2-adic relation ''V''&nbsp;&sube;&nbsp;''R''&nbsp;&times;&nbsp;''S'', and associated with the 2-adic relative term ''v'' whose relate lies in the set ''R'' of real numbers and whose correlate lies in the set ''S'' of syntactic terms.

For now, I will pretend that <math>~v~</math> is a function in <math>\mathbb{R}</math> of <math>~S,~</math> written <math>v : \mathbb{R} \leftarrow S,</math> amounting to the functional alias of the 2-adic relation <math>V \subseteq \mathbb{R} \times S,</math> and associated with the 2-adic relative term <math>~v~</math> whose relate lies in the set <math>\mathbb{R}</math> of real numbers and whose correlate lies in the set <math>~S~</math> of syntactic terms.

===Commentary Note 11.5===

===Commentary Note 11.5===