American Heritage® Dictionary of the English Language, Fourth Edition
- adj. Immeasurably or incalculably minute.
- adj. Mathematics Capable of having values approaching zero as a limit.
- n. An immeasurably or incalculably minute amount or quantity.
- n. Mathematics A function or variable continuously approaching zero as a limit.
Century Dictionary and Cyclopedia
- Infinitely or indefinitely small; less than any assignable quantity.
- n. In mathematics, a fictitious quantity so small that by successive additions to itself no sensible quantity, such as the unit of quantity, could ever be generated. If a is a finite quantity, and i an infinitesimal, we always assume a +
i= a, a fundamental proposition of the infinitesimal calculus; but whether this is because the infinitesimal is a fictitious quantity strictly zero, or because equality is used in a generalized sense in which this is true, is a question of logic, concerning which mathematicians are not agreed. Most writers use the method of limits (which see, under limit), which avoids this and other difficulties. It is assumed that all the mathematical operations can be performed on these quantities. Every power of an infinitesimal is infinitely smaller than any inferior power of the same infinitesimal. (See infinite, 1.) Any infinitesimal may be assumed as a base or standard, by comparison with which the magnitudes of others are estimated. The base itself is said to be of the first order, its square of the second order, its cube of the third order, etc. Finite quantities are of the zero order of infinitesimals, and infinite quantities are generally of negative orders. The logarithm of any infinitesimal of a finite order is of order zero, although it is infinite. In like manner, in every order of infinitesimals there are quantities infinitely greater and quantities infinitely smaller than the power of the base of that order. The square, cube, etc., of an infinitesimal of the zero order remains of the zero order: yet there is nothing peculiar about these infinitesimals; any one of them might have been taken as the base, and then its square would have been reckoned as of the second order, while the infinitesimal in comparison with which it was of the zero order would now appear as of the infinite order.
- adj. Incalculably, exceedingly, or immeasurably minute; vanishingly small.
- adj. mathematics Of or pertaining to values that approach zero as a limit.
- adj. informal Very small.
- n. mathematics A non-zero quantity whose magnitude is smaller than any positive number (by definition it is not a real number).
GNU Webster's 1913
- adj. Infinitely or indefinitely small; less than any assignable quantity or value; very small.
- n. (Math.) An infinitely small quantity; that which is less than any assignable quantity.
- n. (mathematics) a variable that has zero as its limit
- adj. infinitely or immeasurably small
- From New Latin īnfīnītēsimus, infinite in rank, from Latin īnfīnītus, infinite; see infinite. (American Heritage® Dictionary of the English Language, Fourth Edition)
“That is the one and only actual meaning of the use of the term infinitesimal by Leibniz.”
“BTW, "infinitesimal" is an actual word and not made up by Obama.”
“Twice an infinitesimal is an infinitesimal that is twice as big.”
“To Jack from Texas, I know the Texas education system must be in terrible shape with Republicans running that state for so long, but infinitesimal is not a made up word, just do a search, here is the definition:”
“Say, rather, "infinitesimal" - much like the snowflake that starts an avalanche.”
“This has been achieved in two essentially different ways, the one providing a rigorous formulation of the idea of infinitesimal number, the other of infinitesimal magnitude.”
“Bolzano also formulated a definition of the derivative of a function free of the notion of infinitesimal (see Bolzano ).”
“Only by reducing this element of free will to the infinitesimal, that is, by regarding it as an infinitely small quantity, can we convince ourselves of the absolute inaccessibility of the causes, and then instead of seeking causes, history will take the discovery of laws as its problem.”
“In spite of the glowing reports issued annually from various foreign hospitals for natives, and the undeniable good, though desultory and practically infinitesimal, that is being worked by these institutions, we cannot blind ourselves to the fact that western medical science is not making more rapid strides than many other innovations in the great struggle against Chinese prejudice and distrust.”
“In particular, that potent instrument called the infinitesimal calculus, which Newton had invented for the investigation of nature, had become so far perfected that Laplace, when he attempted to unravel the movements of the heavenly bodies, found himself provided with a calculus far more efficient than that which had been available to Newton.”
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