Definitions for theorems
the·o·rems

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1. theorems

   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.

Anagrams for theorems »

1. rest home

How to pronounce theorems?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

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   Tessa

   South African

How to say theorems in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of theorems in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of theorems in Pythagorean Numerology is: 4

Examples of theorems in a Sentence

1. Archimedes:

   Either of my contemporaries or of my successors, will, by means of the method when once established, be able to discover other theorems in addition, which have not yet occurred to me.

2. 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.

3. Lola Thompson:

   So, its really hard to know how much progress this is, because on the one hand its made progress in this direction. But, theres so many equivalent formulations that maybe this direction isnt going to yield the Riemann hypothesis. Maybe one of the other equivalent theorems instead will, if someone can prove one of those.

4. Sarah Hart:

   I am a big fan of giving people as much time as they want to do exams. After all, you never have to prove theorems against the clock in real life so mere speed is not what we want to assess.

5. Alfréd Rényi:

   A mathematician is a device for turning coffee into theorems.

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References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Theorems