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Suppose that X is a vector space over the field of complex or real numbers. Then the set of all linear functionals on X forms a vector space called the algebraic conjugate ...

A Julia set fractal obtained by iterating the function z_(n+1)=c(z_n-sgn(R[z_n])), where sgn(x) is the sign function and R[z] is the real part of z. The plot above sets ...

The region 0<sigma<1, where sigma is defined as the real part of a complex number s=sigma+it. All nontrivial zeros (i.e., those not at negative even integers) of the Riemann ...

A sequence s_n^((lambda))(x)=[h(t)]^lambdas_n(x), where s_n(x) is a Sheffer sequence, h(t) is invertible, and lambda ranges over the real numbers is called a Steffensen ...

A set partition of the rational numbers into two nonempty subsets S_1 and S_2 such that all members of S_1 are less than those of S_2 and such that S_1 has no greatest ...

Dini's theorem is a result in real analysis relating pointwise convergence of sequences of functions to uniform convergence on a closed interval. For an increasing sequence ...

Functional analysis is a branch of mathematics concerned with infinite-dimensional vector spaces (mainly function spaces) and mappings between them. The spaces may be of ...

Hyperreal numbers are an extension of the real numbers to include certain classes of infinite and infinitesimal numbers. A hyperreal number x is said to be finite iff |x|<n ...

A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number ...

A null hypothesis is a statistical hypothesis that is tested for possible rejection under the assumption that it is true (usually that observations are the result of chance). ...