What is theorem?

  • (noun): An idea accepted as a demonstrable truth.
    See also — Additional definitions below


In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms. The derivation of a theorem is often interpreted as a proof of the truth of the resulting expression, but different deductive systems can yield other interpretations, depending on the meanings of the derivation rules. The proof of a mathematical theorem is a logical argument demonstrating that the conclusions are a necessary consequence of the hypotheses, in the sense that if the hypotheses are true then the conclusions must also be true, without any further assumptions. The concept of a theorem is therefore fundamentally deductive, in contrast to the notion of a scientific theory, which is empirical.

Read more about Theorem.

Some articles on theorem:

Robertson–Seymour Theorem
... In graph theory, the Robertson–Seymour theorem (also called the graph minor theorem) states that the undirected graphs, partially ordered by the graph ... set of forbidden minors, in the same way that Wagner's theorem characterizes the planar graphs as being the graphs that do not have the complete graph ... The Robertson–Seymour theorem is named after mathematicians Neil Robertson and Paul D ...
Spectral Theorem
... In mathematics, particularly linear algebra and functional analysis, the spectral theorem is any of a number of results about linear operators or about matrices ... In broad terms the spectral theorem provides conditions under which an operator or a matrix can be diagonalized (that is, represented as a diagonal ... In general, the spectral theorem identifies a class of linear operators that can be modelled by multiplication operators, which are as simple as one can hope to find ...
Spectral Theorem - Bounded Self-adjoint Operators
... and Self-adjoint operator#Spectral theorem The next generalization we consider is that of bounded self-adjoint operators on a Hilbert space ... let A be the operator of multiplication by t on L2, that is Theorem ... such that where T is the multiplication operator and There is also an analogous spectral theorem for bounded normal operators on Hilbert spaces ...
Formalized Account of Theorems - Derivation of A Theorem
... The notion of a theorem is very closely connected to its formal proof (also called a "derivation") ... rule of inference (transformation rule) for is Any occurrence of "A" in a theorem may be replaced by an occurrence of the string "AB" and the result is a theorem ... Theorems in are defined as those formulae which have a derivation ending with that formula ...
Robertson–Seymour Theorem - Finite Form of The Graph Minor Theorem
... Robertson Seymour (1987) showed that the following theorem exhibits the independence phenomenon by being unprovable in various formal systems that are much stronger than Peano ...

More definitions of "theorem":

  • (noun): A proposition deducible from basic postulates.

Famous quotes containing the word theorem:

    To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.
    Albert Camus (1913–1960)