Theorem Meaning: Definition, Examples, and Translations
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theorem
[หฮธiหษrษm ]
Definitions
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 |
|---|---|
| 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 |
|---|---|
| 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
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Interesting Facts
History
- Euclid's 'Elements' contains many early theorems that structure modern geometry today.
- In the 19th century, more complex theorems emerged in areas like calculus and set theory thanks to mathematicians like Gauss and Cantor.
- The 'Fundamental Theorem of Algebra' connects polynomial equations to their roots, showcasing the power of theorems to bridge different areas of math.
Science
- Theorems are vital in physics; for example, the Pythagorean theorem helps calculate distances in mechanics.
- In computer science, theorems establish foundational principles for algorithms and cryptography, proving essential for data security.
- Chaos theory includes theorems that describe complex, unpredictable systems in nature, illustrating the limits of predictability.
Education
- The teaching of theorems helps develop critical thinking skills as students learn to construct logical proofs.
- Many math competitions focus on challenging participants to both use and prove theorems creatively.
- Understanding theorems enhances problem-solving abilities, making students adept at transferring skills across various disciplines.
Pop Culture
- The concept of a theorem appears in popular media, often symbolizing the quest for truth or knowledge.
- Films and books sometimes depict mathematicians working furiously to prove a groundbreaking theorem, highlighting their excitement and dedication.
- The phrase 'the proof is in the pudding' draws a parallel to how a theorem's validity is only established through rigorous proof, much like a recipe.
Origin of 'theorem'
Main points about word origin
- The word 'theorem' comes from the Greek word 'theorema,' meaning 'a thing to be looked at.'
- In ancient times, it referred to a thought or speculation that needed proof or explanation.
- The use of 'theorem' in mathematics dates back to the work of Pythagoras and Euclid.
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.