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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 theory is decidable iff there is an algorithm which can determine whether or not any sentence r is a member of the theory.

The branch of formal logic, also called functional calculus, that deals with representing the logical connections between statements as well as the statements themselves.

Not decidable as a result of being neither formally provable nor unprovable.

Expressions of the form lim_(k->infty)x_0+sqrt(x_1+sqrt(x_2+sqrt(...+x_k))) (1) are called nested radicals. Herschfeld (1935) proved that a nested radical of real nonnegative ...

Given the statement "if P, then Q," or P=>Q, the converse is "if Q, then P." For example, the converse of "If a thing is a dog then it is a mammal" is "If a thing is a mammal ...

The Schröder-Bernstein theorem for numbers states that if n<=m<=n, then m=n. For sets, the theorem states that if there are injections of the set A into the set B and of B ...

The bicommutant theorem is a theorem within the field of functional analysis regarding certain topological properties of function algebras. The theorem says that, given a ...

A right triangle is triangle with an angle of 90 degrees (pi/2 radians). The sides a, b, and c of such a triangle satisfy the Pythagorean theorem a^2+b^2=c^2, (1) where the ...

The converse of Fermat's little theorem is also known as Lehmer's theorem. It states that, if an integer x is prime to m and x^(m-1)=1 (mod m) and there is no integer e<m-1 ...