What does theorem mean?

Definitions for theorem
ˈθi ər əm, ˈθɪər əmthe·o·rem

This dictionary definitions page includes all the possible meanings, example usage and translations of the word theorem.

Princeton's WordNet

  1. theoremnoun

    a proposition deducible from basic postulates

  2. theoremnoun

    an idea accepted as a demonstrable truth

Wiktionary

  1. theoremnoun

    A mathematical statement of some importance that has been proven to be true. Minor theorems are often called propositions. Theorems which are not very interesting in themselves but are an essential part of a bigger theorem's proof are called lemmas

  2. theoremnoun

    A mathematical statement that is expected to be true; as, Fermat's Last Theorem (as which it was known long before it was proved in the 1990s.)

  3. theoremnoun

    a syntactically correct expression that is deducible from the given axioms of a deductive system

  4. theoremverb

    to formulate into a theorem

  5. Etymology: Via theorema, from θεώρημα (Euclid), from θεωρέω, from θεωρός, from θέα + ὁράω. See also theory, and theater.

Samuel Johnson's Dictionary

  1. THEOREMnoun

    A position laid down as an acknowledged truth.

    Etymology: theoreme, Fr. ϑεώρημα.

    Having found this the head theorem of all their discourses, who plead for the change of ecclesiastical government in England, we hold it necessary that the proofs thereof be weighed. Richard Hooker, b. ii.

    The chief points of morality are no less demonstrable than mathematicks; nor is the subtilty greater in moral theorems than in mathematical. Henry More, divine Dialogues.

    Many observations go to the making up of one theorem, which, like oaks fit for durable buildings, must be of many years growth. John Graunt.

    Here are three theorems, that from thence we may draw some conclusions. John Dryden, Dufresnoy.

Wikipedia

  1. 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 the mainstream of 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.

ChatGPT

  1. theorem

    A theorem is a statement or proposition in mathematics or logic that has been proven to be true based on predetermined axioms and logical rules. It is usually a result of a set of accepted statements such as axioms and previously proven theorems. A theorem can also serve as a basis for proving other theorems.

Webster Dictionary

  1. Theoremnoun

    that which is considered and established as a principle; hence, sometimes, a rule

  2. Theoremnoun

    a statement of a principle to be demonstrated

  3. Theoremverb

    to formulate into a theorem

Wikidata

  1. 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 proof of a mathematical theorem is a logical argument demonstrating that the conclusion is a necessary consequence of the hypotheses. This argument is in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the conclusion, but different deductive systems could be interpreted differently, depending on the meanings assigned to the derivation rules. Given such an interpretation of proof as justification of truth, the conclusion is viewed as true in the case that the hypotheses are true, without any further assumptions. In this light, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific theory, which is empirical. Although they can be written in a completely symbolic form using, for example, propositional calculus, theorems are often expressed in a natural language such as English. The same is true of proofs, which are often expressed as logically organized and clearly worded informal arguments, intended to convince readers of the truth of the statement of the theorem beyond any doubt, and from which arguments a formal symbolic proof can in principle be constructed. Such arguments are typically easier to check than purely symbolic ones—indeed, many mathematicians would express a preference for a proof that not only demonstrates the validity of a theorem, but also explains in some way why it is obviously true. In some cases, a picture alone may be sufficient to prove a theorem. Because theorems lie at the core of mathematics, they are also central to its aesthetics. Theorems are often described as being "trivial", or "difficult", or "deep", or even "beautiful". These subjective judgments vary not only from person to person, but also with time: for example, as a proof is simplified or better understood, a theorem that was once difficult may become trivial. On the other hand, a deep theorem may be simply stated, but its proof may involve surprising and subtle connections between disparate areas of mathematics. Fermat's Last Theorem is a particularly well-known example of such a theorem.

Chambers 20th Century Dictionary

  1. Theorem

    thē′ō-rem, n. a proposition to be proved.—adjs. Theoremat′ic, Theorem′ic.—n. Theorem′atīst.—adjs. Theoret′ic, -al, pertaining to theory: not practical: speculative.—adv. Theoret′ically.—n.pl. Theoret′ics, the speculative parts of a science.—n. Thē′oric (Shak.), theory, speculation.—v.i. Thē′orise, to form a theory: to form opinions solely by theories: to speculate.—ns. Thē′orīser; Thē′orist, a theoriser: one given to theory and speculation; Thē′ory, an explanation or system of anything: an exposition of the abstract principles of a science or art: speculation as opposed to practice. [Gr. theōrēmatheōrein, to view—theasthai, to see.]

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Numerology

  1. Chaldean Numerology

    The numerical value of theorem in Chaldean Numerology is: 5

  2. Pythagorean Numerology

    The numerical value of theorem in Pythagorean Numerology is: 3

Examples of theorem in a Sentence

  1. Henri Poincare:

    Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means....[A] machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.

  2. E. Kim Nebeuts:

    To state a theorem and then to show examples is literally to teach backwards.

  3. David Eisenbud:

    The legend around this chalk is that it's impossible to write a false theorem using the chalk, but I think I've disproved that many times.

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Translations for theorem

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"theorem." Definitions.net. STANDS4 LLC, 2024. Web. 26 Feb. 2024. <https://www.definitions.net/definition/theorem>.

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