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A method for computing the prime counting function. Define the function T_k(x,a)=(-1)^(beta_0+beta_1+...+beta_(a-1))|_x/(p_1^(beta_0)p_2^(beta_1)...p_a^(beta_(a-1)))_|, (1) ...

A relation R on a set S is symmetric provided that for every x and y in S we have xRy iff yRx. The symmetric relations on n nodes are isomorphic with the rooted graphs on n ...

A relation R on a set S is irreflexive provided that no element is related to itself; in other words, xRx for no x in S.

A relation R on a set S is reflexive provided that xRx for every x in S.

A reflexive relation.

A relation R on a set S is transitive provided that for all x, y and z in S such that xRy and yRz, we also have xRz.

An almost unit is a nonunit in the integral domain of formal power series with a nonzero first coefficient, P=a_1x+a_2x^2+..., where a_1!=0. Under the operation of ...

Erdős proved that there exist at least one prime of the form 4k+1 and at least one prime of the form 4k+3 between n and 2n for all n>6.

Given a module M over a unit ring R, the set End_R(M) of its module endomorphisms is a ring with respect to the addition of maps, (f+g)(x)=f(x)+g(x), for all x in M, and the ...

A function between categories which maps objects to objects and morphisms to morphisms. Functors exist in both covariant and contravariant types.