What is the difference between infinite and transfinite?

infinite | transfinite | Related terms |

Transfinite is a related term of infinite.

In mathematics terms the difference between infinite and transfinite

is that infinite is greater than any positive quantity or magnitude; limitless while transfinite is relating to transfinite numbers.

As adjectives the difference between infinite and transfinite

is that infinite is indefinably large, countlessly great; immense while transfinite is beyond finite.

As a numeral infinite

is infinitely many.

As a noun transfinite is

a transfinite number.

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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transfinite

English

Adjective

(-)

Beyond finite.

(mathematics) Relating to transfinite numbers.

Noun

(en noun)

A transfinite number.

* Oliver Sacks, Awakenings

An interesting and perhaps essential formal model of this quality is to be found in Cantor's concepts of infinite sets and transfinite cardinals. The laws of ordinary, inductive mathematics do not apply to these, for the 'least part' of such transfinites are equal to the whole, and convey their infinite (i.e. world-like) quality.

References

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