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Arbitrary vs Infinite - What's the difference?

arbitrary | infinite |

In mathematics terms the difference between arbitrary and infinite

is that arbitrary is any and all possible while infinite is greater than any positive quantity or magnitude; limitless.

As adjectives the difference between arbitrary and infinite

is that arbitrary is based on individual discretion or judgment; not based on any objective distinction, perhaps even made at random while infinite is indefinably large, countlessly great; immense.

As a noun arbitrary

is anything arbitrary, such as an arithmetical value or a fee.

As a numeral infinite is

infinitely many.

arbitrary

English

Adjective

(arbitrariness) (en adjective)
  • (usually, of a decision) Based on individual discretion or judgment; not based on any objective distinction, perhaps even made at random.
  • Benjamin Franklin's designation of "positive" and "negative" to different charges was arbitrary . In fact, electrons flow in the opposite direction to conventional current.
    The decision to use 18 years as the legal age of adulthood was arbitrary , as both age 17 and 19 were reasonable alternatives.
  • Determined by impulse rather than reason; heavy-handed.
  • "The Russian trials were Stalin's purges, with which he attempted to consolidate his power. Like most people in the West, I believed these show trials to be the arbitrary acts of a cruel dictator." ( Max Born, Letters to Einstein)
  • (mathematics) Any and all possible.
  • The equation is true for an arbitrary value of x.
  • Determined by independent arbiter.
  • To secure food safety, there should first be a national standard to arbitrarily state what is wholesome and what is not; second, the final buyer should know exactly what he is purchasing. ( The World's Work ...: a history of our time)

    Noun

    (arbitraries)
  • Anything arbitrary, such as an arithmetical value or a fee.
  • infinite

    English

    Adjective

    (en adjective)
  • Indefinably large, countlessly great; immense.
  • * , 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.
  • * (and other bibliographic particulars) H. Brooke
  • 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.
  • * (and other bibliographic particulars) Marlowe
  • infinite riches in a little room
  • * (and other bibliographic particulars) Milton
  • which infinite calamity shall cause to human life
  • Boundless, endless, without end or limits; innumerable.
  • * Bible, Psalms cxlvii. 5
  • Great is our Lord, and of great power; his understanding is infinite .
  • With plural noun: infinitely many.
  • * 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.
  • (mathematics) Greater than any positive quantity or magnitude; limitless.
  • (set theory, of a set) Having infinitely many elements.
  • * {{quote-web
  • , year = 2009 , author = Brandon C. Look , title = Symbolic Logic II, Lecture 2: Set Theory , site = www.uky.edu/~look , url = http://www.uky.edu/~look/Phi520-Lecture7.pdf , accessdate = 2012-11-20 }}
    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.
  • (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

    * amaranthine * boundless * countless * endless * immeasurable * inestimable * interminable * limitless * unbounded * unlimited * vast

    Antonyms

    * finite * infinitesimal * limited

    Hyponyms

    * (set theory) countably infinite * (set theory) uncountable

    Derived terms

    * infinitely * infinitesimal * infinitude * infinity

    Numeral

    (head)
  • Infinitely many.
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