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A paradox or contradiction.

The map which takes points on the surface of a sphere S^2 to their antipodal points.

A quantity which changes sign when indices are reversed. For example, A_(ij)=a_i-a_j is antisymmetric since A_(ij)=-A_(ji).

The application of an apodization function.

If two quantities A and B are approximately equal, this is written A approx B.

A valuation for which |x|<=1 implies |1+x|<=C for the constant C=1 (independent of x). Such a valuation does not satisfy the strong triangle inequality |x+y|<=max(|x|,|y|).

Let a_(n+1) = 1/2(a_n+b_n) (1) b_(n+1) = (2a_nb_n)/(a_n+b_n). (2) Then A(a_0,b_0)=lim_(n->infty)a_n=lim_(n->infty)b_n=sqrt(a_0b_0), (3) which is just the geometric mean.

In logic, a statement which cannot be broken down into smaller statements, also simply called an "atom."

alpha=1/Nsum_(i=1)^N|x_i-mu|=<|x_i-mu|>.

A topological space X in which each subset of X of the "first category" has an empty interior. A topological space which is homeomorphic to a complete metric space is a Baire ...