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The comparability graph of a partially ordered set P=(X,<=) is the graph with vertex set X for which vertices x and y are adjacent iff either x<=y or y<=x in P.

An axiomatic theory (such as a geometry) is said to be complete if each valid statement in the theory is capable of being proven true or false.

The conversion of a quadratic polynomial of the form ax^2+bx+c to the form a(x+b/(2a))^2+(c-(b^2)/(4a)), which, defining B=b/2a and C=c-b^2/4a, simplifies to a(x+B)^2+C.

The set P^2 is the set of all equivalence classes [a,b,c] of ordered triples (a,b,c) in C^3\(0,0,0) under the equivalence relation (a,b,c)∼(a^',b^',c^') if ...

A test which always identifies prime numbers correctly, but may incorrectly identify a composite number as a prime.

The concatenation of two strings a and b is the string ab formed by joining a and b. Thus the concatenation of the strings "book" and "case" is the string "bookcase". The ...

A function f(x) is said to be concave on an interval [a,b] if, for any points x_1 and x_2 in [a,b], the function -f(x) is convex on that interval (Gradshteyn and Ryzhik 2000).

The formal term in propositional calculus for the connective implies.

A transformation of the form g=D^(T)etaD, where det(D)!=0 and det(D) is the determinant. Isometries are also called congruence transformations.

Every compact 3-manifold is the connected sum of a unique collection of prime 3-manifolds.