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In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. In formal set theory, an ordinal ...

A pair of consecutive numbers.

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

An operator of period 2, i.e., an operator * which satisfies ((a)^*)^*=a.

A map which is monotone increasing and therefore order-preserving.

If {f_n} is a sequence of measurable functions, with 0<=f_n<=f_(n+1) for every n, then intlim_(n->infty)f_ndmu=lim_(n->infty)intf_ndmu.

The appropriate notion of integer for surreal numbers.

A simple way to enumerate some types of groups due to J. H. Conway (Zwillinger 1995).

A tensor g whose discriminant satisfies g=g_(11)g_(22)-g_(12)^2>0.