corollary

/kəˈrɒləri/ (bre, ipa) · /ˈkɔːrəleri/ (ame, ipa) · /ˈkȯr-ə-ˌler-ē ˈkär-, -le-rē British kə-ˈrä-lə-rē/ (ame, mw)

corollary — 名詞

  • corollarysingular
  • corollariesplural

1. a fact, situation, or conclusion that grows so directly out of an earlier event

1.名詞C2
釋義

衍生結果

由前事自然帶出的結果

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

例句

The sudden rise in rent was a corollary of the new rail line.

租金突然上漲，是新鐵路線帶來的衍生結果。

a corollary of + earlier change

Longer clinic hours were an unexpected corollary of hiring two more nurses.

診所延長門診時間，是多聘兩名護理師後出現的一個意外結果。

同義詞
  • 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.

反義詞
  • 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

❌Packing an umbrella was a corollary of the weather report.
✅Packing an umbrella was a response to the weather report.
💡corollary names a natural result of an earlier fact, not a personal action someone chooses.
❌Her red scarf was a corollary of the cold weather.
✅Her red scarf was a reaction to the cold weather.
💡use corollary for a consequence or follow-on fact, not for any ordinary choice.

2. in mathematics or logic, a statement you can reach almost at once after an earli

2.名詞C2
釋義

推得命題

由已證命題直接推出的命題

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

例句

After proving the main theorem, Eve wrote a short corollary beneath it.

證完主要定理後，Eve 在下面寫出一個簡短的推得命題。

corollary written after a theorem is proved

The professor said the next corollary followed from Lemma 3 alone.

教授說，下一個推得命題只要根據引理 3 就能得到。

followed from an earlier proved result

同義詞
  • 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.

常見錯誤

❌The class spent a week proving the corollary from first principles.
✅The class spent a week proving the theorem from first principles.
💡a corollary normally follows quickly from an earlier theorem and does not require the same long proof.
❌Our chemistry teacher ended the lesson with a corollary about acids.
✅Our chemistry teacher ended the lesson with a conclusion about acids.
💡this sense belongs to formal reasoning, especially mathematics and logic.