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==Origin==
[http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] ''stricte'', from [[Latin]] ''strictus'', from past participle of ''stringere'' to bind tight
*[http://en.wikipedia.org/wiki/15th_century 15th Century]
==Definitions==
*1archaic: a : tight, close; also : [[intimate]]
:b : narrow
*2a : stringent in requirement or [[control]] <under strict orders>
:b : severe in [[discipline]] <a strict teacher>
*3: a : inflexibly maintained or adhered to <strict [[secrecy]]>
:b : rigorously [[conforming]] to [[principle]] or a norm or condition
*4: exact, [[precise]] <in the strict sense of the word>
*5: of narrow erect [[habit]] of [[growth]] <a strict inflorescence>
==Description==
In [[mathematical]] [[writing]], the adjective '''strict''' is used to [[modify]] technical terms which have multiple [[meanings]]. It indicates that the exclusive meaning of the term is to be understood. (More [[formally]], one could say that this is the meaning which implies the other meanings.) The opposite is non-strict. This is often implicit but can be put explicitly for [[clarity]]. In some [[contexts]] the word "proper" is used as a mathematical synonym for "strict".
This term is commonly used in the [[context]] of [http://en.wikipedia.org/wiki/Inequality_(mathematics) inequalities] — the phrase "strictly less than" means "less than and not equal to" (likewise "strictly greater than" means "greater than and not equal to"). More generally a [http://en.wikipedia.org/wiki/Partially_ordered_set#Strict_and_non-strict_partial_orders strict partial order], [http://en.wikipedia.org/wiki/Strict_total_order strict total order] and [http://en.wikipedia.org/wiki/Strict_weak_ordering strict weak order] exclude [[equality]] and equivalence.
A related use occurs when [[comparing]] numbers to zero — "strictly positive" and "strictly negative" mean "positive and not equal to zero" and "negative and not equal to zero", respectively. Also, in the context of functions, the adverb "strictly " is used to modify the terms "monotonic", "increasing", and "decreasing".
On the other hand, sometimes one wants to specify the [[inclusive]] [[meanings]] of terms. In the context of [[comparisons]], one can use the phrases "non-negative", "non-positive", "non-increasing", and "non-decreasing" to make it [[clear]] that the inclusive sense of the terms is intended.
Using such [[terminology]] helps avoid possible [[ambiguity]] and [[confusion]]. For instance, upon reading the phrase "x is positive", it is not immediately clear whether x = 0 is possible, since some [[authors]] might use the term positive loosely, and mean that x is not less than zero. Therefore, it is prudent to write "x is strictly positive" for x>0 and "x is non-negative" for x≥0. (A precise term like non-negative is never used with the word negative in the wide, loose sense that includes zero.)
The word "proper" is often used in the same way as "strict." For example, a "[http://en.wikipedia.org/wiki/Proper_subset proper subset]" of a set S is a subset that is not equal to S itself, and a "[http://en.wikipedia.org/wiki/Proper_class proper class]" is a class which is not also a set.
[[Category: General Reference]]
[[Category: Mathematics]]
==Origin==
[http://nordan.daynal.org/wiki/index.php?title=English#ca._1100-1500_.09THE_MIDDLE_ENGLISH_PERIOD Middle English] ''stricte'', from [[Latin]] ''strictus'', from past participle of ''stringere'' to bind tight
*[http://en.wikipedia.org/wiki/15th_century 15th Century]
==Definitions==
*1archaic: a : tight, close; also : [[intimate]]
:b : narrow
*2a : stringent in requirement or [[control]] <under strict orders>
:b : severe in [[discipline]] <a strict teacher>
*3: a : inflexibly maintained or adhered to <strict [[secrecy]]>
:b : rigorously [[conforming]] to [[principle]] or a norm or condition
*4: exact, [[precise]] <in the strict sense of the word>
*5: of narrow erect [[habit]] of [[growth]] <a strict inflorescence>
==Description==
In [[mathematical]] [[writing]], the adjective '''strict''' is used to [[modify]] technical terms which have multiple [[meanings]]. It indicates that the exclusive meaning of the term is to be understood. (More [[formally]], one could say that this is the meaning which implies the other meanings.) The opposite is non-strict. This is often implicit but can be put explicitly for [[clarity]]. In some [[contexts]] the word "proper" is used as a mathematical synonym for "strict".
This term is commonly used in the [[context]] of [http://en.wikipedia.org/wiki/Inequality_(mathematics) inequalities] — the phrase "strictly less than" means "less than and not equal to" (likewise "strictly greater than" means "greater than and not equal to"). More generally a [http://en.wikipedia.org/wiki/Partially_ordered_set#Strict_and_non-strict_partial_orders strict partial order], [http://en.wikipedia.org/wiki/Strict_total_order strict total order] and [http://en.wikipedia.org/wiki/Strict_weak_ordering strict weak order] exclude [[equality]] and equivalence.
A related use occurs when [[comparing]] numbers to zero — "strictly positive" and "strictly negative" mean "positive and not equal to zero" and "negative and not equal to zero", respectively. Also, in the context of functions, the adverb "strictly " is used to modify the terms "monotonic", "increasing", and "decreasing".
On the other hand, sometimes one wants to specify the [[inclusive]] [[meanings]] of terms. In the context of [[comparisons]], one can use the phrases "non-negative", "non-positive", "non-increasing", and "non-decreasing" to make it [[clear]] that the inclusive sense of the terms is intended.
Using such [[terminology]] helps avoid possible [[ambiguity]] and [[confusion]]. For instance, upon reading the phrase "x is positive", it is not immediately clear whether x = 0 is possible, since some [[authors]] might use the term positive loosely, and mean that x is not less than zero. Therefore, it is prudent to write "x is strictly positive" for x>0 and "x is non-negative" for x≥0. (A precise term like non-negative is never used with the word negative in the wide, loose sense that includes zero.)
The word "proper" is often used in the same way as "strict." For example, a "[http://en.wikipedia.org/wiki/Proper_subset proper subset]" of a set S is a subset that is not equal to S itself, and a "[http://en.wikipedia.org/wiki/Proper_class proper class]" is a class which is not also a set.
[[Category: General Reference]]
[[Category: Mathematics]]
