Theorem: meaning, definitions and examples

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theorem

 

[ หˆฮธiหษ™rษ™m ]

Noun
Context #1 | Noun

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

law, principle, proposition.

Which Synonym Should You Choose?

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Word Description / Examples
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.

  • Pythagoras' theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
  • The theorem was derived after extensive proofs were validated.
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.

  • The proposition that all swans are white was disproven when black swans were discovered.
  • He presented a business proposition to the investors.
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.

  • The principle of conservation of energy states that energy cannot be created or destroyed, only transformed.
  • She is a person of strong moral principles, always standing up for what she believes in.
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.

  • Newton's first law of motion states that an object will remain at rest or in uniform motion unless acted upon by an external force.
  • The law prohibits stealing and ensures that justice is served.

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.
Context #2 | Noun

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

axiom, postulate, principle.

Which Synonym Should You Choose?

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Word Description / Examples
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.

  • Pythagoras' theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
  • Euclid's Theorem on the infinitude of prime numbers is a fundamental concept in number theory.
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.

  • The principle of conservation of energy states that energy cannot be created or destroyed, only transformed.
  • One of the key principles of democratic societies is the right to freedom of speech.
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.

  • In Euclidean geometry, one of the axioms is that through any two points, there is exactly one straight line.
  • The axiom of equality states that things which are equal to the same thing are also equal to one another.
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.

  • One of Euclidโ€™s postulates is that a straight line segment can be drawn joining any two points.
  • Einsteinโ€™s theory of relativity includes the postulate that the speed of light in a vacuum is constant.

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:

๐Ÿ‡ต๐Ÿ‡น teorema

๐Ÿ‡ฎ๐Ÿ‡ณ เคชเฅเคฐเคฎเฅ‡เคฏ

๐Ÿ‡ฉ๐Ÿ‡ช Theorem

๐Ÿ‡ฎ๐Ÿ‡ฉ teorema

๐Ÿ‡บ๐Ÿ‡ฆ ั‚ะตะพั€ะตะผะฐ

๐Ÿ‡ต๐Ÿ‡ฑ twierdzenie

๐Ÿ‡ฏ๐Ÿ‡ต ๅฎš็† (ใฆใ„ใ‚Š)

๐Ÿ‡ซ๐Ÿ‡ท thรฉorรจme

๐Ÿ‡ช๐Ÿ‡ธ teorema

๐Ÿ‡น๐Ÿ‡ท teorem

๐Ÿ‡ฐ๐Ÿ‡ท ์ •๋ฆฌ (jeong-ri)

๐Ÿ‡ธ๐Ÿ‡ฆ ู†ูŽุธูŽุฑููŠูŽู‘ุฉ

๐Ÿ‡จ๐Ÿ‡ฟ teorรฉm

๐Ÿ‡ธ๐Ÿ‡ฐ teorรฉma

๐Ÿ‡จ๐Ÿ‡ณ ๅฎš็† (dรฌnglว)

๐Ÿ‡ธ๐Ÿ‡ฎ teorema

๐Ÿ‡ฎ๐Ÿ‡ธ frรฆรฐi

๐Ÿ‡ฐ๐Ÿ‡ฟ ั‚ะตะพั€ะตะผะฐ

๐Ÿ‡ฌ๐Ÿ‡ช แƒ—แƒ”แƒแƒ แƒ”แƒ›แƒ (teorema)

๐Ÿ‡ฆ๐Ÿ‡ฟ teorema

๐Ÿ‡ฒ๐Ÿ‡ฝ 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.

Word Frequency Rank

At #6,108 in frequency, this word belongs to advanced vocabulary. It's less common than core vocabulary but important for sophisticated expression.