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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.

A point which lies on at least one ordinary line is called an ordinary point, or sometimes a regular point.

A surface which is homeomorphic to a finite collection of spheres, each with a finite number of handles, cross-handles, cross-caps, and perforations. A preliminary version of ...

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 ...

A regular surface M subset R^n is called orientable if each tangent space M_p has a complex structure J_p:M_p->M_p such that p->J_p is a continuous function.

A nonsingular linear map A:R^n->R^n is orientation-preserving if det(A)>0.

The oriented matroid of a finite configuration of points extracts relative position and orientation information from the configuration. An oriented matroid can be described ...

The central point (r=0) in polar coordinates, or the point with all zero coordinates (0, ..., 0) in Cartesian coordinates. In three dimensions, the x-axis, y-axis, and z-axis ...