Category vs Continuum - What's the difference?
category | continuum |
A group, often named or numbered, to which items are assigned based on similarity or defined criteria.
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(mathematics) A collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative.
A continuous series or whole, no part of which is noticeably different from its adjacent parts, although the ends or extremes of it are very different from each other.
A continuous extent.
* {{quote-magazine, date=2012-03
, author=(Henry Petroski)
, title=Opening Doors
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(mathematics) The set of all real numbers and, more generally, a compact connected metric space.
(musical instruments) A touch-sensitive strip, similar to an electronic standard musical keyboard, except that the note steps are of a semitone, and so are not separately marked.
In mathematics terms the difference between category and continuum
is that category is a collection of objects, together with a transitively closed collection of composable arrows between them, such that every object has an identity arrow, and such that arrow composition is associative while continuum is the set of all real numbers and, more generally, a compact connected metric space.As nouns the difference between category and continuum
is that category is a group, often named or numbered, to which items are assigned based on similarity or defined criteria while continuum is a continuous series or whole, no part of which is noticeably different from its adjacent parts, although the ends or extremes of it are very different from each other.category
English
(wikipedia category)Noun
(categories)- The traditional way of describing the similarities and differences between constituents is to say that they belong to categories'' of various types. Thus, words like ''boy'', ''girl'', ''man'', ''woman'', etc. are traditionally said to belong to the category''' of Nouns, whereas words like ''a'', ''the'', ''this'', and ''that'' are traditionally said to belong to the ' category of Determiners.
- This steep and dangerous climb belongs to the most difficult category .
- I wouldn't put this book in the same category as the author's first novel.
- One well-known category has sets as objects and functions as arrows.
- Just as a monoid consists of an underlying set with a binary operation "on top of it" which is closed, associative and with an identity, a category consists of an underlying digraph with an arrow composition operation "on top of it" which is transitively closed, associative, and with an identity at each object. In fact, a category's composition operation, when restricted to a single one of its objects, turns that object's set of arrows (which would all be loops) into a monoid.
Synonyms
* (group to which items are assigned) class, family, genus, group, kingdom, order, phylum, race, tribe, type * See alsoDerived terms
* category mistake * category theory * conceptual category * perceptual category * subcategory * supercategoryExternal links
* *continuum
English
(wikipedia continuum)Noun
(en-noun)citation, passage=A doorknob of whatever roundish shape is effectively a continuum of levers, with the axis of the latching mechanism—known as the spindle—being the fulcrum about which the turning takes place.}}
