theorem - ορισμός. Τι είναι το theorem
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Τι (ποιος) είναι theorem - ορισμός

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
  • planar]] map with five colors such that no two regions with the same color meet. It can actually be colored in this way with only four colors. The [[four color theorem]] states that such colorings are possible for any planar map, but every known proof involves a computational search that is too long to check by hand.
  • universality]]) resembles the [[Mandelbrot set]].
  • strings of symbols]] may be broadly divided into [[nonsense]] and [[well-formed formula]]s. A formal language can be thought of as identical to the set of its well-formed formulas. The set of well-formed formulas may be broadly divided into theorems and non-theorems.
  • publisher=[[Institute of Education Sciences]] (IES) of the [[U.S. Department of Education]] }}  Originally published in 1940 and reprinted in 1968 by National Council of Teachers of Mathematics.</ref>

theorem         
n.
1) to deduce, formulate a theorem
2) to prove; test a theorem
3) a binomial theorem
theorem         
(theorems)
A theorem is a statement in mathematics or logic that can be proved to be true by reasoning.
N-COUNT
theorem         
['???r?m]
¦ noun Physics & Mathematics a general proposition not self-evident but proved by a chain of reasoning.
?a rule in algebra or other branches of mathematics expressed by symbols or formulae.
Derivatives
theorematic -'mat?k adjective
Origin
C16: from Fr. theoreme, or via late L. from Gk theorema 'speculation, proposition'.

Βικιπαίδεια

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.

Παραδείγματα από το σώμα κειμένου για theorem
1. "Before dozing off to sleep, I think about how to prove a theorem," he said.
2. "The Last Theorem," co–written with Frederik Pohl, will be published later this year, it said.
3. Simon Singh is author of Big Bang and Fermats Last Theorem
4. According to that thinking, alongside the only–in–Israel theorem there was an Israel–is–different axiom.
5. The Government snoopers are to be taught Pythagoras‘s Theorem and algebraic equations in readiness for a Labour property tax revaluation.