theorem - определение. Что такое theorem
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Что (кто) такое theorem - определение

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>
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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'.
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.
Proposition (to be demonstrated), position, dictum, thesis.
Divergence theorem         
  • n}}
  • A volume divided into two subvolumes. At right the two subvolumes are separated to show the flux out of the different surfaces.
  • The volume can be divided into any number of subvolumes and the flux out of ''V'' is equal to the sum of the flux out of each subvolume, because the flux through the <span style="color:green;">green</span> surfaces cancels out in the sum. In (b) the volumes are shown separated slightly, illustrating that each green partition is part of the boundary of two adjacent volumes
  • </math> approaches <math>\operatorname{div} \mathbf{F}</math>
  • The divergence theorem can be used to calculate a flux through a [[closed surface]] that fully encloses a volume, like any of the surfaces on the left. It can ''not'' directly be used to calculate the flux through surfaces with boundaries, like those on the right. (Surfaces are blue, boundaries are red.)
  • The vector field corresponding to the example shown. Vectors may point into or out of the sphere.
GENERALIZATION OF THE FUNDAMENTAL THEOREM IN VECTOR CALCULUS
Gauss' theorem; Gauss's theorem; Gauss theorem; Ostrogradsky-Gauss theorem; Ostrogradsky's theorem; Gauss's Theorem; Divergence Theorem; Gauss' divergence theorem; Ostrogradsky theorem; Gauss-Ostrogradsky theorem; Gauss Ostrogradsky theorem; Gauss–Ostrogradsky theorem
In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.
Thévenin's theorem         
  • Norton-Thevenin conversion
THEOREM IN ELECTRICAL CIRCUIT ANALYSIS
Thevenin generator; Thévenin equivalent; Thevenin equivalent; Thevenin's theorem; Thèvenin equivalent; Thèvenin's theorem; Thévenin's theorem (electric networks); Thevanin equivalent; Thevenin theorem; Thévenin theorem; Thevenins theorem; Thévenin circuit; Thévenin terminator; Thevenin Equivalent; Thevenin terminator; Thevenin circuit; Thevenin's theorem (electric networks); Thevenin's Theorem; Equivalent voltage source; Helmholtz–Thévenin theorem; Helmholtz-Thévenin theorem; Helmholtz–Thevenin theorem; Helmholtz-Thevenin theorem; Helmholtz' source theorem; Helmholtz' source superposition theorem; Helmholtz' superposition theorem; Helmholtz' superposition; Helmholtz source theorem; Helmholtz source superposition theorem; Helmholtz superposition theorem; Helmholtz superposition; Superposition principle by Helmholtz; Superposition theorem by Helmholtz
As originally stated in terms of direct-current resistive circuits only, Thévenin's theorem states that "For any linear electrical network containing only voltage sources, current sources and resistances can be replaced at terminals A–B by an equivalent combination of a voltage source Vth in a series connection with a resistance Rth."
Ehrenfest theorem         
THEOREM THAT THE TIME EVOLUTION OF THE EXPECTATION VALUE OF A QUANTUM OBSERVABLE IS PROPORTIONAL TO THAT OF THE COMMUTATOR BETWEEN THE OBSERVABLE AND THE HAMILTONIAN (PLUS THAT OF ANY EXPLICIT TIME DEPENDENCE OF THE OPERATOR, IF ANY)
Ehrenfest's theorem; Ehrenfest Theorem; Ehrenfest Principle; Ehrenfest's Theorem
The Ehrenfest theorem, named after Paul Ehrenfest, an Austrian theoretical physicist at Leiden University, relates the time derivative of the expectation values of the position and momentum operators x and p to the expectation value of the force F=-V'(x) on a massive particle moving in a scalar potential V(x), Section 3.7.
Hilton's theorem         
THEOREM THAT THE BASED LOOP SPACE OF A WEDGE OF SPHERES IS HOMOTOPY-EQUIVALENT TO A PRODUCT OF LOOP SPACES OF SPHERES
Hilton theorem; Hilton–Milnor theorem; Hilton-Milnor theorem
In algebraic topology, Hilton's theorem, proved by , states that the loop space of a wedge of spheres is homotopy-equivalent to a product of loop spaces of spheres.
Poynting's theorem         
THEOREM IN PHYSICS, SHOWING THE CONSERVATION OF ENERGY FOR THE ELECTROMAGNETIC FIELD, EXPRESSED IN THE FORM OF A PARTIAL DIFFERENTIAL EQUATION DEVELOPED BY BRITISH PHYSICIST JOHN HENRY POYNTING
Poynting Theorem; Poynting theorem
In electrodynamics, Poynting's theorem is a statement of conservation of energy for electromagnetic fields developed by British physicist John Henry Poynting. It states that in a given volume, the stored energy changes at a rate given by the work done on the charges within the volume, minus the rate at which energy leaves the volume.

Википедия

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.