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One of the Zermelo-Fraenkel axioms which asserts the existence of the empty set emptyset. The axiom may be stated symbolically as exists x forall y(!y in x).

The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the ...

The word basis can arise in several different contexts. Speaking in general terms, an object is "generated" by a basis in whatever manner is appropriate. For example, a ...

One baud is defined as the state of a signal in a communication channel changing once per second.

A convergence test also called "de Morgan's and Bertrand's test." If the ratio of terms of a series {a_n}_(n=1)^infty can be written in the form ...

Johnson solid J_(50).

Possessing two modes. The term bimodal distribution, which refers to a distribution having two local maxima (as opposed to two equal most common values) is a slight ...

If a field has the property that, if the sets A_1, ..., A_n, ... belong to it, then so do the sets A_1+...+A_n+... and A_1...A_n..., then the field is called a Borel field ...

A (symmetrical) boundary set of radius r and center x_0 is the set of all points x such that |x-x_0|=r. Let x_0 be the origin. In R^1, the boundary set is then the pair of ...

The function Pi_(a,b)(x)=H(x-a)-H(x-b) which is equal to 1 for a<=x<=b and 0 otherwise. Here H(x) is the Heaviside step function. The special case Pi_(-1/2,1/2)(x) gives the ...