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One of the operations exists exists (called the existential quantifier) or for all forall (called the universal quantifier, or sometimes, the general quantifier). However, ...

Each row and each column in the group multiplication table lists each of the group elements once and only once. From this, it follows that no two elements may be in the ...

Any system of phi(n) integers, where phi(n) is the totient function, representing all the residue classes relatively prime to n is called a reduced residue system (Nagell ...

A function is termed regular iff it is analytic and single-valued throughout a region R.

If two algebraic plane curves with only ordinary singular points and cusps are related such that the coordinates of a point on either are rational functions of a ...

Associated with an irreducible curve of curve genus p, there are p linearly independent integrals of the first sort. The roots of the integrands are groups of the canonical ...

Every continuous linear functional U[f] for f in C[a,b] can be expressed as a Stieltjes integral U[f]=int_a^bf(x)dw(x), where w(x) is determined by U and is of bounded ...

A circular cone the centers of whose sections form a line perpendicular to the bases. When used without qualification, the term "cone" often refers to a right circular cone.

A graph G whose line graph is L(G) is called the root graph R(L(G)) of L(G). In order words, R(L(G))=G. The root graph of a connected graph is unique except for K_3=C_3 (the ...

The divisibility test that an integer is divisible by 9 iff the sum of its digits is divisible by 9.