(0) Not
�is a frequently used suffix or prefix keyword modifier.
Not[True] is False.
Not[Not[expr]] is equivalent to expr.
Not[function] is function�s inverse.
If number is any Real or Cardinal, then
Not[number]
�is the negative number.
Not[set]
�is the PatternSet whose elements are not in (do not match) set.
Not[Reckon][expr]
�causes expr to not be reckoned if it is a subExpression in a larger evaluation.
If set is a Named Set, and test is an element,
Not[Set[set]][test]
�removes test from set and returns True.
If test is not in set, False is returned.
See English Definition for "not".
If a �function� is any purposeful expression, then by convention,
(1) Not[function]
�is the form used to represent that purposeful function�s inverse.
This means for any expr, (an Expression), the following should be true:
(2) Not[Not[expr]] is equivalent to expr.
The rest of this keyword specification lists various �Not[�]� inverse-functions.
By definition, Not[True] is False:
If number is a Real or a Cardinal, then
�is the negative value of number.
If set is a PatternSet, then�
�is the PatternSet of anything which is not in (does not match) �set�.
If el is in some element of (or matches) set, then Not[�set�][el] will return False.
(6) Not[Reckon][expr_Expression]
�causes expr to not be reckoned if it is a subExpression in an evaluation.
Not[Reckon][expr] is a wrapper which protects expr from being reckoned.
A SubstitutionName assigned in an elicitation is the only exception. An elicitation may use a SubstitutionName to substitute values into expr in (6), but otherwise it will not be interpreted.
A PatternSet will be interpreted literally if it is wrapped in Not[Reckon][patSet]. Specifically, if patSet is a PatternSet and�
�is a subExpression in a PatternForm, then patSet will be treated literally like everything else in the PatternForm (that is not a Pattern[�]).
The dispositive Set function removes Set elements. It is the inverse of �Set[set]�.
Specifically, if test is an expression in the named Set, �set�, then�
Set[set][test]
�adds test to �set�, if it is not already a member.
The inverse removes test if it is a member. Formally,
(8) Not[Set[set]][test]
�removes test from set and returns True. If test is not in set, False is returned.
not adv.
An adverbial particle expressing negation;
�corresponding to the attributive no. As used with verbs, when immediately after or before a simple tense or form of an ordinary verb it is now archaic and chiefly poetic; as,
"that which satisfieth not.";
"all that not harms distinctive womanhood."
It is used commonly either with an auxiliary verb or with the substantive verb be, in both cases immediately following; as,
"Thou shalt not steal."
When used with an infinitive or verbal noun in �ing, it precedes. When preceding negative adjectives or adverbs, esp. those formed with un-, in-, im-, etc., it serves in expressing a degree of comparison less than the positive; as, not unnatural; not implausibly.
--not a little. To a considerable extent or degree. -- not but. Only. Cf. NOBBUT. Obs. � not guilty.
Law. The words of general issue, used to deny the whole declaration or indictment, in various actions. � not half. Not at all. �ironically. Colloq. British. not half. or so, bad. Rather good. Colloq. � not out. See 2d CRICKET, n., 1. �not proved, or, now more commonly not proven. Scots Law. The verdict brought in by a jury who finds that the charges made are not proved. It operates as an acquittal.
� 2004, 2005
by John Van Wie Bergamini
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