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A counterexample is a form of counter proof. Given a hypothesis stating that F(x) is true for all x in S, show that there exists a b in S such that F(b) is false, ...

An exponent is the power p in an expression of the form a^p. The process of performing the operation of raising a base to a given power is known as exponentiation.

A number of the form 2^n-1 obtained by setting x=1 in a Fermat-Lucas polynomial, more commonly known as a Mersenne number.

The field of rationals is the set of rational numbers, which form a field. This field is commonly denoted Q (doublestruck Q).

The field of reals is the set of real numbers, which form a field. This field is commonly denoted R (doublestruck R).

If it is possible to transform a coordinate system to a form where the metric elements g_(munu) are constants independent of x^mu, then the space is flat.

A congruence of the form f(x)=g(x) (mod n), where f(x) and g(x) are both integer polynomials. Functional congruences are sometimes also called "identical congruences" (Nagell ...

The set of all ground atoms that can be formed from predicate symbols from a clause in Skolemized form S and terms from the Herbrand universe H of S.

A ring that is commutative under multiplication, has a multiplicative identity element, and has no divisors of 0. The integers form an integral domain.

A discrete distribution of a random variable such that every possible value can be represented in the form a+bn, where a,b!=0 and n is an integer.