# Infinitesimal vs Infinite - What's the difference?

infinitesimal | infinite | Antonyms |

## In context|mathematics|lang=en terms the difference between infinitesimal and infinite

is that infinitesimal is (mathematics) a non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number) while infinite is (mathematics) greater than any positive quantity or magnitude; limitless.

## As adjectives the difference between infinitesimal and infinite

is that infinitesimal is incalculably, exceedingly, or immeasurably minute; vanishingly small while infinite is indefinably large, countlessly great; immense.

## As a noun infinitesimal

is (mathematics) a non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).

infinitely many.

# infinitesimal

## English

• Incalculably, exceedingly, or immeasurably minute; vanishingly small.
• *
• (mathematics) Of or pertaining to values that approach zero as a limit.
• (informal) Very small.
• #### Usage notes

* Strictly, this adjective, like infinite, is incomparable, so more infinitesimal' and '''most infinitesimal are proscribed, especially in the mathematical sense. However, these forms do occur in informal usage, where the ''very small (but measurable) sense is most common.

#### Antonyms

* infinite * enormous

### Noun

(wikipedia infinitesimal) (en noun)
• (mathematics) A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).

* infinity

#### Derived terms

* infinitesimal calculus * infinitesimally

# infinite

## English

• 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