in⋅fin⋅i⋅tes⋅i⋅mal
[in-fin-i-tes-uh-muh
l]
| 1. | indefinitely or exceedingly small; minute: infinitesimal vessels in the circulatory system. |
| 2. | immeasurably small; less than an assignable quantity: to an infinitesimal degree. |
| 3. | of, pertaining to, or involving infinitesimals. |
| 4. | an infinitesimal quantity. |
| 5. | Mathematics. a variable having zero as a limit. |
Based on the Random House Dictionary, © Random House, Inc. 2009.
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Copyright © 2009 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Infinitesimal
In`fin*i*tes"i*mal\, a. [Cf. F. infinit['e]simal, fr. infinit['e]sime infinitely small, fr. L. infinitus. See Infinite, a.] Infinitely or indefinitely small; less than any assignable quantity or value; very small. Infinitesimal calculus, the different and the integral calculus, when developed according to the method used by Leibnitz, who regarded the increments given to variables as infinitesimal.Infinitesimal
In`fin*i*tes"i*mal\, n. (Math.) An infinitely small quantity; that which is less than any assignable quantity.Cite This Source
infinitesimal (adj.)
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| infinitesimal (ĭn'fĭn-ĭ-těs'ə-məl) Pronunciation Key
Adjective Capable of having values approaching zero as a limit. Noun A function or variable continuously approaching zero as a limit. |
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infinitesimal
in mathematics, a quantity less than any finite quantity yet not zero. Even though no such quantity can exist in the real number system, many early attempts to justify calculus were based on sometimes dubious reasoning about infinitesimals: derivatives were defined as ultimate ratios of infinitesimals, and integrals were calculated by summing rectangles of infinitesimal width. As a result, differential and integral calculus was originally referred to as the infinitesimal calculus. This terminology gradually disappeared as rigorous concepts of limit, continuity, and the real numbers were formulated.
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