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Directory:Jon Awbrey/Papers/Peirce's 1870 Logic Of Relatives (view source)
Revision as of 21:40, 3 December 2007
, 21:40, 3 December 2007→Commentary Note 11.9: markup
Also, we introduced a few bits of additional terminology and special-purpose notations for working with tubular relations:
Also, we introduced a few bits of additional terminology and special-purpose notations for working with tubular relations:
<blockquote>
{| cellpadding="4"
| ''P'' is a "pre-function" ''P'' : ''X'' ~> ''Y''
| ''P'' is a "pre-function" ''P'' : ''X'' ~> ''Y''
| iff
| iff
| ''P'' is tubular at ''Y''.
| ''P'' is tubular at ''Y''.
|}
|}
</blockquote>
Thus, we arrive by way of this winding stair at the very special stamps of 2-adic relations ''P'' ⊆ ''X'' × ''Y'' that are "total prefunctions" at ''X'' (or ''Y''), "total and tubular" at ''X'' (or ''Y''), or "1-regular" at ''X'' (or ''Y''), more often celebrated as "functions" at ''X'' (or ''Y'').
Thus, we arrive by way of this winding stair at the very special stamps of 2-adic relations ''P'' ⊆ ''X'' × ''Y'' that are "total prefunctions" at ''X'' (or ''Y''), "total and tubular" at ''X'' (or ''Y''), or "1-regular" at ''X'' (or ''Y''), more often celebrated as "functions" at ''X'' (or ''Y'').
<p>To say that a relation ''P'' ⊆ ''X'' × ''Y'' is totally tubular at ''X'' is to say that it is 1-regular at ''X''. Thus, we may formalize the following definitions:</p>
<p>To say that a relation ''P'' ⊆ ''X'' × ''Y'' is totally tubular at ''X'' is to say that it is 1-regular at ''X''. Thus, we may formalize the following definitions:</p>
{| cellpadding="4"
| ''P'' is a "function" ''p'' : ''X'' → ''Y''
| ''P'' is a "function" ''p'' : ''X'' → ''Y''
| iff
| iff