corollary
/kəˈrɒləri/ (bre, ipa) · /ˈkɔːrəleri/ (ame, ipa) · /ˈkȯr-ə-ˌler-ē ˈkär-, -le-rē British kə-ˈrä-lə-rē/ (ame, mw)
corollary — noun
- corollarysingular
- corollariesplural
1. a fact, situation, or conclusion that grows so directly out of an earlier event
a fact, situation, or conclusion that grows so directly out of an earlier event or idea that it seems like an expected follow-on effect
The sudden rise in rent was a corollary of the new rail line.
a corollary of + earlier change
Longer clinic hours were an unexpected corollary of hiring two more nurses.
For Bilal, daily back pain was a corollary of years of warehouse lifting.
Cheaper phone plans became one corollary of the fierce price war.
A packed bus station was the corollary of canceling every morning train.
- consequence
More common and often used for negative results; corollary is more formal and sometimes more neutral.
- outcome
A broader word for any final result, without the same sense of a tightly linked follow-on.
- spin-off
More informal and often used for a useful extra effect rather than a logical consequence.
- cause
Names the earlier event or fact that produces the later result.
文法句型
a corollary of + noun phrase
be a corollary of + noun phrase
用法筆記
Most often used in writing or formal speech when one change naturally brings another. It is usually followed by of plus the earlier fact or event. Distinguish it from result: corollary is more formal and suggests the link is easy to see once the first fact is accepted.
常見錯誤
2. in mathematics or logic, a statement you can reach almost at once after an earli
in mathematics or logic, a statement you can reach almost at once after an earlier claim has been established, needing only a very small extra step
After proving the main theorem, Eve wrote a short corollary beneath it.
corollary written after a theorem is proved
The professor said the next corollary followed from Lemma 3 alone.
followed from an earlier proved result
Iris checked whether the corollary still held when the angle changed.
In Gabriel's notes, each corollary was boxed in blue beside the proof.
The class proved one corollary about circles before lunch on Friday.
- inference
A broader term for something concluded from evidence or reasoning; corollary is narrower and tied to a proved result.
- deduction
Focuses on the reasoning process, while corollary names the statement reached at the end.
- logical consequence
A close technical equivalent, though corollary especially suggests a result that follows with very little additional work.
文法句型
a corollary to + theorem
derive a corollary from + theorem
prove a corollary
用法筆記
Used in mathematics and logic. A corollary is not the main theorem itself; it is a later statement that drops out quickly once the theorem has been established. Common verbs with this sense include prove, derive, follow from, and state.