Search results
Results from the WOW.Com Content Network
Higher-order programming is a style of computer programming that uses software components, like functions, modules or objects, as values. It is usually instantiated with, or borrowed from, models of computation such as lambda calculus which make heavy use of higher-order functions. A programming language can be considered higher-order if ...
In common speech, an infinitesimal object is an object that is smaller than any feasible measurement, but not zero in size—or, so small that it cannot be distinguished from zero by any available means. Hence, when used as an adjective in mathematics, infinitesimal means infinitely small, smaller than any standard real number. Infinitesimals ...
The only properties that differ between the reals and the hyperreals are those that rely on quantification over sets, or other higher-level structures such as functions and relations, which are typically constructed out of sets. Each real set, function, and relation has its natural hyperreal extension, satisfying the same first-order properties.
Cardinal numbers define the size of sets, meaning how many members they contain, and can be standardized by choosing the first ordinal number of a certain size to represent the cardinal number of that size. The smallest ordinal infinity is that of the positive integers, and any set which has the cardinality of the integers is countably infinite.
Higher-order thinking, also known as higher order thinking skills (HOTS), [1] is a concept applied in relation to education reform and based on learning taxonomies (such as American psychologist Benjamin Bloom's taxonomy). The idea is that some types of learning require more cognitive processing than others, but also have more generalized benefits.
The most salient deformation theory in mathematics has been that of complex manifolds and algebraic varieties.This was put on a firm basis by foundational work of Kunihiko Kodaira and Donald C. Spencer, after deformation techniques had received a great deal of more tentative application in the Italian school of algebraic geometry.
The real contributions of nonstandard analysis lie however in the concepts and theorems that utilize the new extended language of nonstandard set theory. Among the list of new applications in mathematics there are new approaches to probability, [ 11 ] hydrodynamics, [ 21 ] measure theory, [ 22 ] nonsmooth and harmonic analysis, [ 23 ] etc.
In mathematics, nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus.It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic.