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A metric space X is isometric to a metric space Y if there is a bijection f between X and Y that preserves distances. That is, d(a,b)=d(f(a),f(b)). In the context of ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

Let a triangle have sides of length a, b, and c and let the angles opposite these sides be denoted A, B, and C. The law of tangents states ...

A nonnegative measurable function f is called Lebesgue integrable if its Lebesgue integral intfdmu is finite. An arbitrary measurable function is integrable if f^+ and f^- ...

A problem related to the continuum hypothesis which was solved by Solovay (1970) using the inaccessible cardinals axiom. It has been proven by Shelah and Woodin (1990) that ...

A method for generating random (pseudorandom) numbers using the linear recurrence relation X_(n+1)=aX_n+c (mod m), where a and c must assume certain fixed values, m is some ...

There are at least two distinct notions of linear space throughout mathematics. The term linear space is most commonly used within functional analysis as a synonym of the ...

A bounded entire function in the complex plane C is constant. The fundamental theorem of algebra follows as a simple corollary.

A locus is the set of all points (usually forming a curve or surface) satisfying some condition. For example, the locus of points in the plane equidistant from a given point ...

Machin's formula is given by 1/4pi=4cot^(-1)5-cot^(-1)239. There are a whole class of Machin-like formulas with various numbers of terms (although only four such formulas ...