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Aleph-1 is the set theory symbol aleph_1 for the smallest infinite set larger than aleph_0 (Aleph-0), which in turn is equal to the cardinal number of the set of countable ...

A function representable as a generalized Fourier series. Let R be a metric space with metric rho(x,y). Following Bohr (1947), a continuous function x(t) for (-infty<t<infty) ...

In floating-point arithmetic, a biased exponent is the result of adding some constant (called the bias) to the exponent chosen to make the range of the exponent nonnegative. ...

A searching algorithm which works on a sorted table by testing the middle of an interval, eliminating the half of the table in which the key cannot lie, and then repeating ...

If a continuous function defined on an interval is sometimes positive and sometimes negative, it must be 0 at some point. Bolzano (1817) proved the theorem (which effectively ...

A Cartesian product of any finite or infinite set I of copies of Z_2, equipped with the product topology derived from the discrete topology of Z_2. It is denoted Z_2^I. The ...

Let g:R->R be a function and let h>0, and define the cardinal series of g with respect to the interval h as the formal series sum_(k=-infty)^inftyg(kh)sinc((x-kh)/h), where ...

A check which can be used to verify correct computations in a table of grouped classes. For example, consider the following table with specified class limits and frequencies ...

A Gaussian quadrature-like formula over the interval [-1,1] which has weighting function W(x)=x. The general formula is int_(-1)^1xf(x)dx=sum_(i=1)^nw_i[f(x_i)-f(-x_i)]. n ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It uses weighting function W(x)=1 in the interval [-1,1] and forces all the weights to be equal. The ...