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An algorithm which constructs allowed mathematical statements from simple ingredients.

The symmetry operation (x,y,z)->(x,y,-z), etc., which is equivalent to 2^_, where the bar denotes an improper rotation.

A surface given by the form z=F(x,y).

A mathematical structure (e.g., a group, vector space, or smooth manifold) in a category.

A geometry constructed without reference to measurement. The only primitive concepts are those of points and intermediacy. There are 10 axioms underlying ordered geometry.

A cupolarotunda in which the bases are in the same orientation.

The image of the path gamma in C under the function f is called the trace. This usage of the term "trace" is unrelated to the same term applied to matrices or tensors.

A fractal process for which H>1/2, so r>0.

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

A measure that takes on real values.