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If a is an element of a field F over the prime field P, then the set of all rational functions of a with coefficients in P is a field derived from P by adjunction of a.

An operator * for which a*b=-b*a is said to be anticommutative.

For operators A^~ and B^~, the anticommutator is defined by {A^~,B^~}=A^~B^~+B^~A^~.

If a map f:G->G^' from a group G to a group G^' satisfies f(ab)=f(b)f(a) for all a,b in G, then f is said to be an antihomomorphism.

The antilaplacian of u with respect to x is a function whose Laplacian with respect to x equals u. The antilaplacian is never unique.

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

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|).

An "area" which can be defined for every set--even those without a true geometric area--which is rigid and finitely additive.

If O_(p^')(G)=1 and if x is a p-element of G, then L_(p^')(C_G(x))<=E(C_G(x)), where L_(p^') is the p-layer.

A determinant appearing in Padé approximant identities: C_(r/s)=|a_(r-s+1) a_(r-s+2) ... a_r; | | ... |; a_r a_(r+1) ... a_(r+s-1)|.