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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). ...

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

The y- (vertical) coordinate of a point in a two dimensional coordinate system. Physicists and astronomers sometimes use the term to refer to the axis itself instead of the ...

A manifold is said to be orientable if it can be given an orientation. Note the distinction between an "orientable manifold" and an "oriented manifold," where the former ...

An important result in ergodic theory. It states that any two "Bernoulli schemes" with the same measure-theoretic entropy are measure-theoretically isomorphic.

The ordinary differential equation

An orthogonal array OA(k,s) is a k×s^2 array with entries taken from an s-set S having the property that in any two rows, each ordered pair of symbols from S occurs exactly ...

An orthogonal basis of vectors is a set of vectors {x_j} that satisfy x_jx_k=C_(jk)delta_(jk) and x^mux_nu=C_nu^mudelta_nu^mu, where C_(jk), C_nu^mu are constants (not ...

Two functions f(x) and g(x) are orthogonal over the interval a<=x<=b with weighting function w(x) if <f(x)|g(x)>=int_a^bf(x)g(x)w(x)dx=0. (1) If, in addition, ...

Two representations of a group chi_i and chi_j are said to be orthogonal if sum_(R)chi_i(R)chi_j(R)=0 for i!=j, where the sum is over all elements R of the representation.