MyWikiBiz, Author Your Legacy — Wednesday July 03, 2024
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, 21:40, 3 December 2007
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| 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: |
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− | :{| cellpadding="4"
| + | <blockquote> |
| + | {| cellpadding="4" |
| | ''P'' is a "pre-function" ''P'' : ''X'' ~> ''Y'' | | | ''P'' is a "pre-function" ''P'' : ''X'' ~> ''Y'' |
| | iff | | | iff |
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| | ''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''). |
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| <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> |
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− | :{| cellpadding="4"
| + | {| cellpadding="4" |
| | ''P'' is a "function" ''p'' : ''X'' → ''Y'' | | | ''P'' is a "function" ''p'' : ''X'' → ''Y'' |
| | iff | | | iff |