corollary

/kə'rɔləri/

Thân thiện

A successful proof often leads to a useful corollary.

Definition

1. Noun:
   • (Logic) An inference that follows directly from the proof of another proposition: In logic and mathematics, a "corollary" is a statement that can be deduced with little or no additional proof from a theorem or proposition that has already been proven.
   • A practical consequence that follows naturally: More generally, a "corollary" is a natural, direct, or inevitable result or consequence of a fact, action, or condition.

Examples of Usage

• Noun (Logical Inference):

  • The corollary of the theorem was used to solve the more complex problem.
  • If two angles of a triangle are equal, a corollary is that the sides opposite those angles are also equal.

• Noun (Natural Consequence):

  • A corollary of increased economic growth is often higher employment.
  • One corollary of the new privacy law is that companies must be more transparent about data collection.

Advanced Usage

• "as a corollary (to/of)": used to introduce a statement that is a direct result of something previously mentioned.
  • As a corollary to the main argument, we can conclude that the policy is unsustainable.
  • His resignation was a direct corollary of the scandal.

Variants and Related Words

• Corollaries (n): The plural form of "corollary".
  • The paper listed three important corollaries of the central hypothesis.

Synonyms

• Consequence: A result or effect of an action or condition.
• Result: A thing that is caused or produced by something else.
• Implication: A conclusion that can be drawn from something, although it is not explicitly stated.
• Deduction: A conclusion reached on the basis of evidence and reasoning.

Related Phrases

• Necessary corollary: An unavoidable or inescapable consequence.
  • Increased risk is a necessary corollary of high-reward investments.

Related Idioms

• "Go with the corollary": (Less common) To accept or acknowledge the natural consequence of a position or decision. This is a specialized usage.
  • If you support free market principles, you must go with the corollary that some businesses will fail.

Học thuật

Noun

1. (logic) an inference that follows directly from the proof of another proposition
2. a practical consequence that follows naturally
   • blind jealousy is a frequent corollary of passionate love