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An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...

Consecutive numbers (or more properly, consecutive integers) are integers n_1 and n_2 such that n_2-n_1=1, i.e., n_2 follows immediately after n_1. Given two consecutive ...

A generalization of Poncelet's continuity principle made by H. Schubert in 1874-1879. The conservation of number principle asserts that the number of solutions of any ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

A theorem in set theory stating that, for all sets A and B, the following equivalences hold, A subset B<=>A intersection B=A<=>A union B=B.

A polynomial P(x) that, when evaluated over each x in the domain of definition, results in the same value. The simplest example is P(x)=c for x in R and c a constant.

A function f(x) is said to be constructible if some algorithm F computes it, in binary, within volume O(f(x)), i.e., V_(F(x))=O(f(x)). Here, the volume V_(A(x)) is the ...

A formal argument in logic in which it is stated that (1) P=>Q and R=>S (where => means "implies"), and (2) either P or R is true, from which two statements it follows that ...

The contact angle between a sphere and a tangent plane is the angle alpha between the normal to the sphere at the point of tangency and the basal plane with respect to which ...

A partition p is said to contain another partition q if the Ferrers diagram of p contains the Ferrers diagram of q. For example, {3,3,2} (left figure) contains both {3,3,1} ...