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Let lim stand for the limit lim_(x->c), lim_(x->c^-), lim_(x->c^+), lim_(x->infty), or lim_(x->-infty), and suppose that lim f(x) and lim g(x) are both zero or are both ...

A q-analog, also called a q-extension or q-generalization, is a mathematical expression parameterized by a quantity q that generalizes a known expression and reduces to the ...

A short mnemonic for remembering the first seven decimal digits of pi is "How I wish I could calculate pi" (C. Heckman, pers. comm., Feb. 3, 2005). Eight digits are given by ...

Comprehensive encyclopedia of mathematics with 13,000 detailed entries. Continually updated, extensively illustrated, and with interactive examples.

A quadratic form Q(x) is indefinite if it is less than 0 for some values and greater than 0 for others. The quadratic form, written in the form (x,Ax), is indefinite if ...

The middle levels conjecture, also known as revolving door conjecture, posits that the middle layer graph has a Hamilton cycle for every n>=1. The conjecture was proved by ...

If a is an element of a field F over the prime field P, then the set of all rational functions of a with coefficients in P is a field derived from P by adjunction of a.

A quantity which changes sign when indices are reversed. For example, A_(ij)=a_i-a_j is antisymmetric since A_(ij)=-A_(ji).

An "area" which can be defined for every set--even those without a true geometric area--which is rigid and finitely additive.

Let P be a polynomial of degree n with derivative P^'. Then ||P^'||_infty<=n||P||_infty, where ||P||_infty=max_(|z|=1)|P(z)|.