different between infinite vs transfinite

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)

1. 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
2. Boundless, endless, without end or limits; innumerable. [from 15th c.]

   • Great is our Lord, and of great power; his understanding is infinite.

3. (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.

4. (mathematics) Greater than any positive quantity or magnitude; limitless. [from 17th c.]
5. (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.

6. (grammar) Not limited by person or number. [from 19th c.]
7. (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

1. Infinitely many.

Noun

infinite (plural infinites)

1. 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.

References

Italian

Adjective

infinite

1. feminine plural of infinito

Latin

Adjective

?nf?n?te

1. 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

English

Etymology

From German transfinit, coined by Georg Cantor

Pronunciation

• IPA^(key): /t?æns?fa?na?t/

Adjective

transfinite (not comparable)

1. Beyond finite.
2. (mathematics) Relating to transfinite numbers.

Derived terms

• transfinitely

Related terms

• finite
• infinite
• transfinity

Translations

Noun

transfinite (plural transfinites)

1. A transfinite number.

References

German

Pronunciation

Adjective

transfinite

1. inflection of transfinit:
   1. strong/mixed nominative/accusative feminine singular
   2. strong nominative/accusative plural
   3. weak nominative all-gender singular
   4. weak accusative feminine/neuter singular

Italian

Adjective

transfinite

1. feminine plural of transfinito