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Qu'est-ce (qui) est THEOREMS - définition

IN MATHEMATICS, A STATEMENT THAT HAS BEEN PROVED

Theorems; Proposition (mathematics); Theorum; Mathematical theorem; Logical theorem; Formal theorem; Theorem (logic); Mathematical proposition; Hypothesis of a theorem

theorem

n.

Proposition (to be demonstrated), position, dictum, thesis.

Theorem

·vt To formulate into a theorem.

II. Theorem ·noun A statement of a principle to be demonstrated.

III. Theorem ·noun That which is considered and established as a principle; hence, sometimes, a rule.

theorem

n.

1) to deduce, formulate a theorem

2) to prove; test a theorem

3) a binomial theorem

Wikipédia

Theorem

In mathematics, a theorem is a statement that has been proved, or can be proved. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.

In mainstream mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as theorems only the most important results, and use the terms lemma, proposition and corollary for less important theorems.

In mathematical logic, the concepts of theorems and proofs have been formalized in order to allow mathematical reasoning about them. In this context, statements become well-formed formulas of some formal language. A theory consists of some basis statements called axioms, and some deducing rules (sometimes included in the axioms). The theorems of the theory are the statements that can be derived from the axioms by using the deducing rules. This formalization led to proof theory, which allows proving general theorems about theorems and proofs. In particular, Gödel's incompleteness theorems show that every consistent theory containing the natural numbers has true statements on natural numbers that are not theorems of the theory (that is they cannot be proved inside the theory).

As the axioms are often abstractions of properties of the physical world, theorems may be considered as expressing some truth, but in contrast to the notion of a scientific law, which is experimental, the justification of the truth of a theorem is purely deductive.

https://en.wikipedia.org/wiki/Theorem

Exemples du corpus de texte pour THEOREMS

1. Kantorovich, the only Russian to win the Nobel Prize for economics, had to pay more than once in Soviet times for the fact that his mathematical theorems occupied such an important role in economics.

2. However, the image of the modernist composer as white–coated scientist dealing with difficult concepts, theorems and technology is not one that has done much to promote the popular image of Bach.

3. On his third attempt he found a sympathetic GH Hardy, who preferred the poor and disadvantaged to the "confident, booming, imperialist bourgeois English". According to most accounts, Hardy initially thought Ramanujan‘s 10–page letter, containing over 100 statements of mathematical theorems, was a prank.

4. It‘s a brilliant way to help the reader develop fondness for the pursuit of mathematics without resorting to actual mathematical theorem and proof (although theorems are discussed as well). Stewart hints, for instance, at the marvelous story of Wiles proving Fermat‘s last theorem.