On the other hand, if the road is short enough to see in its entirety but loops in on itself, we could say that its length is 'infinite'.Ī term I came up with for this is 'supermaximum' above the maximum possible measured value. For example, the question 'how long is this road?' may have the answer 'the opposite of infinitesimal' if we lack the capacity to travel along a straight road in its entirety and measure its length. ‘The book shows how this notion can be used to form various kinds of infinities such as the projective plane, transfinite numbers, and infinitesimals. ‘These two concepts, infinitesimals and infinite quantities, however, were stirring great philosophical dilemmas.’. Infinity is an abstract concept for something that never ends, not merely a value above measuring capability. An indefinitely small quantity a value approaching zero. 'Infinite' is not the opposite of infinitesimal, although that term is commonly (mis)used. Notice how the symbol d appears as the 'result' of the limiting process from. the definition of a derivative: (1) f ( x) d f ( x) d x lim x 0 f ( x) x, where we denote. Analogously, if we have a 100 centimeter ruler, then any length measured longer than 100 cm is that opposite term. The differentials are the artifacts that remain from the way we define derivatives and integrals. The opposite of infinitesimal means a value larger than the maximum possible measurement. For example, if we have a ruler with 1 centimeter intervals, then any length measured shorter than 1 cm is infinitesimal for that measuring instrument - smaller than the smallest possible measurement, but still greater than zero. Much colloquial usage undoubtedly emerges from the humorous hyperbole of declaring something impossibly small, by people aware of the mathematical meaning.Infinitesimal means a value smaller than the minimum possible measurement.

For the lay person, a convenient definition of the mathematical usage is impossibly small. Mathematicians know there is no such thing as the smallest non-zero number, but this idiomatic fiction spares them from impossibly complex descriptions. The infinitesimal value is the fictional smallest of all numbers, which results, impossibly, in the limit being calculated. Thus the only real infinitesimal is zero. In calculus, a calculation can get ever closer to a known result, the limit, as one of its component values gets ever closer to zero but there is no actual value small enough to produce that result. R in which one can rigorously define infinitesimals: e E R is infinitesimal if -a < e < a for all positive a E R. The mathematical usage is very difficult to grasp for a non-expert, because the infinitesimal value is a fiction that represents an abstract concept with a convenient idiom.However, these forms do occur in informal usage, where the very small (but measurable) sense is most common. Find more words Another word for, Opposite of, Meaning of, Rhymes with, Sentences with, Find word forms, Pronounce, Translate from English, Translate to. Strictly, this adjective, like infinite, is incomparable, so more infinitesimal and most infinitesimal are proscribed, especially in the mathematical sense.The usual meaning of the word continuous is unbroken or uninterrupted: thus a. ( mathematics ) Of or pertaining to values that approach zero as a limit. The continuum concept is one of the oldest in mathematics and philosophy.Rather, it shattered into infinitesimal pieces. But the particular verb doesn't do the action justice. Then you could say that the doorway exploded.

Infinitesimals def