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The number of "arrangements" in an ordering of n items is given by either a combination (order is ignored) or a permutation (order is significant). An ordering (or order) is ...

The four of Hilbert's axioms which concern the arrangement of points.

Physicists and engineers use the phrase "order of magnitude" to refer to the smallest power of ten needed to represent a quantity. Two quantities A and B which are within ...

Let (A,<=) and (B,<=) be disjoint totally ordered sets with order types alpha and beta. Then the ordinal sum is defined at set (C=A union B,<=) where, if c_1 and c_2 are both ...

Let (A,<=) and (B,<=) be well ordered sets with ordinal numbers alpha and beta. Then alpha<beta iff A is order isomorphic to an initial segment of B (Dauben 1990, p. 199). ...

Let alpha and beta be any ordinal numbers, then ordinal exponentiation is defined so that if beta=0 then alpha^beta=1. If beta is not a limit ordinal, then choose gamma such ...

Let (A,<=) and (B,<=) be totally ordered sets. Let C=A×B be the Cartesian product and define order as follows. For any a_1,a_2 in A and b_1,b_2 in B, 1. If a_1<a_2, then ...

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 ...

An ordinary differential equation (frequently called an "ODE," "diff eq," or "diffy Q") is an equality involving a function and its derivatives. An ODE of order n is an ...

An ordinary differential equation of order n is an equation of the form F(x,y,y^',...,y^((n)))=0.