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Let X=(X,tau) be a topological vector space whose continuous dual X^* may or may not separate points (i.e., may or may not be T2). The weak-* (pronounced "weak star") ...

The Weingarten equations express the derivatives of the normal vector to a surface using derivatives of the position vector. Let x:U->R^3 be a regular patch, then the shape ...

Szemerédi's theorem states that every sequence of integers that has positive upper Banach density contains arbitrarily long arithmetic progressions. A corollary states that, ...

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. More ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

A quantity to be added to another, also called a summand. For example, in the expression a+b+c, a, b, and c are all addends. The first of several addends, or "the one to ...

A formal mathematical theory which introduces "components at infinity" by defining a new type of divisor class group of integers of a number field. The divisor class group is ...

Arnauld's paradox states that if negative numbers exist, then (-1)/1 must equal 1/(-1), which asserts that the ratio of a smaller to a larger quantity equals the ratio of the ...

1 calcus=1/(2304).

Given an arithmetic series {a_1,a_1+d,a_1+2d,...}, the number d is called the common difference associated to the sequence.