corollary - Master This Word
Master this word with our 5-step learning method – Learn English in English
corollary Word Meanings
- a proposition that follows from one already proved
- a result or consequence of something
- something that results from or is supplementary to a main idea
corollary Example Sentences
Example sentences are the start of understanding. Don't rush to memorize. First feel how the word works in a sentence.
corollary Phonetic & Pronunciation
UK
/kəˈrɒləri/
US
/kəˈrɑːləri/
corollary Word Etymology
Root decomposition: 'coroll-' (a crown or garland) + '-ary' (related to). Historical origin: Latin 'corollarium' (gift of a garland) → Old French 'corollaire' → English. Memory image: Imagine a flower's crown given as a reward, representing truths that naturally follow one another like petals unfolding.
Note 1: These definitions and etymologies are not standard dictionary definitions, but extended explanations provided to help with memorization and understanding of the actual application of words. Through this background information, we strive to make words more vivid and easier to understand, and help you remember their meanings in real life.
Note 2: LexiTalk designs the learning flow around the linguistics principle of “Comprehensible Input.” When learners encounter material that is slightly above their level but still understandable from context, the brain naturally absorbs the language. That’s why we keep every word inside authentic contexts, using examples and associations to help you understand it and use it flexibly.
Read the FAQ explanation of Comprehensible InputReal Context
Corollary is a noun meaning a proposition that follows from a previously proved statement, often seen as a natural, almost self-evident consequence. It signals a secondary result that extends the main idea without needing a new proof. In math, a corollary is a specific, direct consequence of a theorem; outside math, the term can describe any logical outcome that naturally arises from a central argument or plan. Effective use emphasizes its connection to the original proof: a corollary is not a guess, but a dependable, derived truth that follows from the established work. Remember the memory image of a crown-like garnish extending the main idea like petals.
Usage Reminders
- Think of corollary as a natural consequence of a proven result.
- Use it to label a direct, often simpler consequence.
- Don’t introduce a new proof for a corollary.
- Differentiate corollary from a lemma or proposition.
- Keep the focus on the relationship between the main theorem and its corollary.
Common Misconceptions
- Corollary is any consequence derived from an argument, not necessarily tied to a theorem.
- A corollary requires a new proof as if it were a separate result.
- Corollary and lemma are interchangeable terms.
- All conclusions in discussions are corollaries.
- Corollary is weaker or less important than the main theorem by default.
Thinking Differences
Corollary is a compact label for a natural consequence; English academic usage often emphasizes its link to the proven theorem and treats it as a derivative rather than a separate claim.
Learning Tips
- Read the main theorem first to spot possible corollaries.
- Identify the logical steps that lead directly to the corollary.
- Practice naming corollaries in proofs with clear link phrases.
- Differentiate corollary, lemma, and proposition by their roles.
- Create a diagram showing how the corollary follows from the theorem.
- Use corollaries to test understanding of the theorem.
5-Step Learning Method - Learn English in English
Step 1: Meaning
What is the definition of 'corollary'?
A.A type of animal found in tropical regions.
B.A consequence or result derived from a previously established fact or principle.
C.A method of solving mathematical equations.
D.A form of entertainment involving performance and music.
Step 2: Usage
Identify the correct usage of 'corollary' in a sentence.
A.The corollary of his argument was an unexpected conclusion.
B.She enjoyed the corollary book she picked up at the library.
C.After the storm, the corollary left debris everywhere.
D.He failed the exam because he did not understand the corollary formula.
Step 3: Similar Words
Which word is most similar to 'corollary'?
A.Violation
B.Antonym
C.Result
D.Compression
Step 4: Opposite Words
What is the opposite of 'corollary'?
A.Source
B.Contradiction
C.Foundation
D.Consequence
Step 5: Mastery
Can you think of a real-life context where the term 'corollary' might be used?
A.If the law changes, there will likely be new consequences for citizens.
B.The findings showed that climate change has several related effects on biodiversity.
C.Higher education is often seen as a corollary to increased earning potential.
D.The study concluded that increased pollution levels have a significant impact.
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