different between infinite vs compactification
infinite
English
Etymology
From Latin inf?n?tus, from in- (“not”) + f?nis (“end”) + the perfect passive participle ending -itus.
Pronunciation
- (UK) IPA(key): /??nf?n?t/
- (US) IPA(key): /??nf?n?t/, /??nf?n?t/
- Hyphenation: in?fi?nite
Adjective
infinite (comparative more infinite, superlative most infinite)
- Indefinably large, countlessly great; immense. [from 14th c.]
- 1735, Henry Brooke, Universal Beauty
- Whatever is finite, as finite, will admit of no comparative relation with infinity; for whatever is less than infinite is still infinitely distant from infinity; and lower than infinite distance the lowest or least cannot sink.
- }}
- infinite riches in a little room
- 1735, Henry Brooke, Universal Beauty
- Boundless, endless, without end or limits; innumerable. [from 15th c.]
- Great is our Lord, and of great power; his understanding is infinite.
- (with plural noun) Infinitely many. [from 15th c.]
- 2012, Helen Donelan, Karen Kear, Magnus Ramage, Online Communication and Collaboration: A Reader
- Huxley's theory says that if you provide infinite monkeys with infinite typewriters, some monkey somewhere will eventually create a masterpiece – a play by Shakespeare, a Platonic dialogue, or an economic treatise by Adam Smith.
- 2012, Helen Donelan, Karen Kear, Magnus Ramage, Online Communication and Collaboration: A Reader
- (mathematics) Greater than any positive quantity or magnitude; limitless. [from 17th c.]
- (set theory, of a set) Having infinitely many elements.
- For any infinite set, there is a 1-1 correspondence between it and at least one of its proper subsets. For example, there is a 1-1 correspondence between the set of natural numbers and the set of squares of natural numbers, which is a proper subset of the set of natural numbers.
- (grammar) Not limited by person or number. [from 19th c.]
- (music) Capable of endless repetition; said of certain forms of the canon, also called perpetual fugues, constructed so that their ends lead to their beginnings.
Usage notes
Although the term is incomparable in the precise sense, it can be comparable both in mathematics and set theory to compare different degrees of infinity, and informally to denote yet a larger thing.
Poets (and particularly hymn-writers before the 20th century) would commonly rhyme the word as though pronounced [-??n??t] and church congregations still on occasion adopt that pronunciation.
Synonyms
- (indefinably large): immeasurable, inestimable, vast
- (without end or limits): amaranthine, boundless, endless, interminable, limitless, unbounded, unending, unlimited; see also Thesaurus:infinite or Thesaurus:eternal
- (infinitely many): countless; see also Thesaurus:innumerable
Antonyms
- finite
- infinitesimal
- limited
Hyponyms
- (set theory): countably infinite
- (set theory): uncountable
Derived terms
Related terms
- infinitive
Translations
Numeral
infinite
- Infinitely many.
Noun
infinite (plural infinites)
- Something that is infinite in nature.
- 2004, Teun Koetsier, Luc Bergmans, Mathematics and the Divine: A Historical Study (page 449)
- Cautiously, Hobbes avoided asserting the equality of these infinites, and explicitly characterized the relation between them as non-inequality.
- 2004, Teun Koetsier, Luc Bergmans, Mathematics and the Divine: A Historical Study (page 449)
References
Italian
Adjective
infinite
- feminine plural of infinito
Latin
Adjective
?nf?n?te
- vocative masculine singular of ?nf?n?tus
References
- infinite in Charlton T. Lewis and Charles Short (1879) A Latin Dictionary, Oxford: Clarendon Press
- infinite in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
- infinite in Gaffiot, Félix (1934) Dictionnaire illustré Latin-Français, Hachette
infinite From the web:
- what infinite mean
- what infinite set
- what infinite heart's ease
- what indefinitely means
- what's infinite solutions
- what's infinitely many solutions
- what's infinite jest about
- what's infinite lists real name
compactification
English
Etymology
compact +? -ification
Noun
compactification (plural compactifications)
- (topology) Any of various procedures of enlarging a topological space to make it compact.
- (topology) The space resulting from any such procedure.
- (physics) Any modification of a theory such that an infinite parameter becomes finite
Derived terms
- Freund-Rubin compactification
- Wallman compactification
Translations
Further reading
- compactification on Wikipedia.Wikipedia
compactification From the web:
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