• Infinite

    Pronunciation

    • UK IPA: /ˈɪnfɪnɪt/
    • US IPA: /ˈɪnfɪnɪt/, /ˈɪnfÉ™nɪt/

    Origin

    From Latin infinitus, from in- ("not") + finis ("end") + the perfect passive participle ending -itus.

    Full definition of infinite

    Adjective

    infinite

    1. Indefinably large, countlessly great; immense. from 14th c.
      • 1603, John Florio, trans. Michel de Montaigne, Essays, I.40:The number is so infinite, that verily it would be an easier matter for me to reckon up those that have feared the same.
      • unknown date H. BrookeWhatever 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.
      • unknown date Marloweinfinite riches in a little room
      • unknown date Miltonwhich infinite calamity shall cause to human life
    2. Boundless, endless, without end or limits; innumerable. from 15th c.
      • Bible, Psalms cxlvii. 5Great is our Lord, and of great power; his understanding is infinite.
    3. (now rare) With plural noun: infinitely many. from 15th c.
    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.

    Synonyms

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    Related terms

    Numeral

    numeral

    1. Infinitely many.
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