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In mathematics education, Finite Mathematics is a syllabus in college and university mathematics that is independent of calculus. A course in precalculus may be a prerequisite for Finite Mathematics.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
In mathematics, a series is, roughly speaking, an addition of infinitely many terms, one after the other. [1] The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures in combinatorics through generating functions.
Another position was endorsed by David Hilbert: finite mathematical objects are concrete objects, infinite mathematical objects are ideal objects, and accepting ideal mathematical objects does not cause a problem regarding finite mathematical objects. More formally, Hilbert believed that it is possible to show that any theorem about finite ...
Among the axioms of Zermelo–Fraenkel set theory, on which most of modern mathematics can be developed, is the axiom of infinity, which guarantees the existence of infinite sets. [1] The mathematical concept of infinity and the manipulation of infinite sets are widely used in mathematics, even in areas such as combinatorics that may seem to ...
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. [a] Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time ...
Set theory is the branch of mathematics that studies sets, which are collections of objects, such as {blue, white, red} or the (infinite) set of all prime numbers. Partially ordered sets and sets with other relations have applications in several areas. In discrete mathematics, countable sets (including finite sets) are the main focus
A set of real numbers (hollow and filled circles), a subset of (filled circles), and the infimum of . Note that for totally ordered finite sets, the infimum and the minimum are equal. A set A {\displaystyle A} of real numbers (blue circles), a set of upper bounds of A {\displaystyle A} (red diamond and circles), and the smallest such upper ...