Theorem: meaning, definitions and examples
๐
theorem
[ หฮธiหษrษm ]
mathematics
A theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted facts. The proof of a theorem is a logical argument that uses these established statements and facts to demonstrate the truth of the statement being proven.
Synonyms
Which Synonym Should You Choose?
Word | Description / Examples |
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theorem |
Used primarily in mathematics and logic. It is a statement or proposition that has been proven based on previously established statements and accepted logical principles.
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proposition |
Used in logic, mathematics, and general discussion. It is a statement or assertion that expresses a judgement or opinion, often subject to proof or disproof.
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principle |
Used in various fields including science, philosophy, and ethics. It refers to a foundational concept or rule that serves as the basis for a system of belief or behavior.
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law |
Used in science, legal contexts, and social systems. In science, it is a statement based on repeated experimental observations that describes some aspect of the world. In legal and social contexts, it refers to a system of rules recognized as regulating the actions of members.
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Examples of usage
- A classic example of a theorem in mathematics is the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
- Another famous theorem is the Fundamental Theorem of Calculus, which relates the concept of differentiation and integration in calculus.
general
A theorem can also refer to a general statement or principle that is accepted as a truth based on empirical evidence or logical reasoning, but may not have a formal proof.
Synonyms
Which Synonym Should You Choose?
Word | Description / Examples |
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theorem |
A theorem is a statement that has been proven to be true based on previously established statements, such as other theorems, axioms, and postulates. It is commonly used in mathematics.
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principle |
A principle is a fundamental truth or proposition that serves as the foundation for a system of belief, behavior, or reasoning. It is often used in broader contexts beyond mathematics, such as in science, ethics, and philosophy.
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axiom |
An axiom is a statement that is accepted as true without proof. It forms the basis for other statements and reasoning in a theoretical framework, particularly in mathematics and logic.
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postulate |
A postulate is similar to an axiom but is typically used to describe basic assumptions within a specific theory, such as the starting points in geometry. It is something assumed without proof to be true within a given context.
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Examples of usage
- It is a widely accepted theorem in psychology that individuals tend to conform to social norms in group settings.
- One common business theorem is that lower prices lead to higher sales volume.
Translations
Translations of the word "theorem" in other languages:
๐ต๐น teorema
๐ฎ๐ณ เคชเฅเคฐเคฎเฅเคฏ
๐ฉ๐ช Theorem
๐ฎ๐ฉ teorema
๐บ๐ฆ ัะตะพัะตะผะฐ
๐ต๐ฑ twierdzenie
๐ฏ๐ต ๅฎ็ (ใฆใใ)
๐ซ๐ท thรฉorรจme
๐ช๐ธ teorema
๐น๐ท teorem
๐ฐ๐ท ์ ๋ฆฌ (jeong-ri)
๐ธ๐ฆ ููุธูุฑููููุฉ
๐จ๐ฟ teorรฉm
๐ธ๐ฐ teorรฉma
๐จ๐ณ ๅฎ็ (dรฌnglว)
๐ธ๐ฎ teorema
๐ฎ๐ธ frรฆรฐi
๐ฐ๐ฟ ัะตะพัะตะผะฐ
๐ฌ๐ช แแแแ แแแ (teorema)
๐ฆ๐ฟ teorema
๐ฒ๐ฝ teorema
Etymology
The word "theorem" originated from the Greek word "theorema", which means "a spectacle" or "that which is looked at". In ancient Greece, a theorem referred to a mathematical or geometrical statement that could be demonstrated or proved. Over time, the term has evolved to encompass general principles and statements beyond mathematics.
See also: theoretic, theoretical, theorist, theorize.