## Theorem

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*.

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### Some articles on theorem:

**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 ...

**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 ...

**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 ...

**Theorem**s - 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 ...

**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)