# 數學文獻中的片語
###### tags: `數學`
[TOC]

## 參考
* [Glossary of Proof Terms](https://faculty.cord.edu/ahendric/2011Fall325/Glossary.pdf)

## 定理、證明
| 台漢 | 台羅 | 英語 |
| -------- | ---------------------- | -------------------- |
| 關係式 | kuan-hē-sik | relation |
| 數學式 | sòo-ha̍k-sik | expression |
| 公式 | kong-sik | formula |
| 恆等式 | hîng-tíng-sik | identity |
| 定義 | tīng-gī | definition |
| 法則 | huat-tsik | rule |
| 定律 | tīng-lu̍t | law |
| 原理 | guân-lí | principle |
| ==公理== | kong-lí | axiom <br> postulate |
| 定理 | tīng-lí | theorem |
| 命題 | bīng-tê | proposition |
| ==補題== | póo-tê | lemma |
| ==系理== | hē-lí | corollary |
| ==[推想](https://chhoe.taigi.info/MaryknollEngtaiSutian/9528)== <br> ==[臆說](https://chhoe.taigi.info/TaijitToaSutian/15577)== | tshui-sióng<br>ik-suat | conjecture |
| | | paradox |
| 條件 | tiâu-kiānn | condition |
| 結論 | kiat-lūn | conclusion |
| 推論 | tshui-lūn | derive |
| 證明 | | prove, verify, show |
| 算、求 | | calculate,estimate |
| 解 | | solve |
| | | generalization |
| | | in general |
| | | specifically |
| | | case |

## 解
| 台漢 | 台羅 | 英語 |
| -------- | ---------------- | ------------ |
| 平平零 | pênn-pênn lîng | vanish |
| 非零的 | hui-lîng ê | nonvanishing |
| 平凡的 | pîng-huân ê | trivial |
| 非平凡的 | hui-pîng-huang ê | non-trivial |

## 演算
| 台漢 | 台羅 | 英語 |
| -------------------------- | ---------------------------------- | ----------------------------------------------- |
| | | Let... |
| | | Set... |
| | | Put... |
| | | differentiate |
| | | integrate |
| | | combine |
| 共 A 式橐入去 B 式（內底） | kā A sik lok ji̍p-ì B sik (lāi-té) | substitute Eq. A in Eq. B<br>put Eq. A in Eq. B |
| 其中 | kî-tiong | ..., where... |
| 重寫 | tîng-siá | rewrite |
| 寫現現 | siá hiān-hiān | write explicitly |
| 是寫做按呢： | sī siá tsò án-ne: | is given by |
| 形式是按呢： | hîng-sik sī án-ne: | is of the form... |

## 論證
| 台漢 | 台羅 | 英語 |
| ----------- | ----------------- | ------------------------------------- |
| 設使 | siat-sú | assuming (that)..., suppose (that)... |
| 佇……的都合 | tī ... ê too-ha̍p | provided (that)... |
| 根據 | kin-kì | according to |
| | | result from |
| 造成、致使 | tsō-sîng, tì-sú | result in<br>lead to |
| 因為 | in-uī | because, since |
| 所致、[所擺](https://chhoe.taigi.info/iTaigiHoataiTuichiautian/7536) | sóo-tì, sóo-pái | hence, therfore |
| （就）得着 | (tiō) tit-tio̍h | we obtain ... |
| 就知 | tiō tsai | we have ... |
| （就）得着 | (tiō) tit-tio̍h | we find ... |
| （就）得着 | (tiō) tit-tio̍h | we obtain ... |
| 結果是 | kiat-kó sī | it follows that ... |
| | | it can be seen that... |
| 是誠實-\-兮 | sī tsiânn-si̍t--ê | is true |
| 有成立 | ū sîng-li̍p | stands |
| A 佮 B 會合 | A kah B ē ha̍h | A satisfies B |
| A 佮 B 袂合 | A kah B bē ha̍h | A does not satisfy B |
| | | Q.E.D. |

### 嚇驚式證明（[Proof by intimidation](https://en.wikipedia.org/wiki/Proof_by_intimidation)）
| 台漢 | 台羅 | 英語 |
| -------------- | ---- | --------------------------------- |
| | | Clearly... |
| | | It is self-evident that... |
| | | It can be easily shown that... |
| | | ... does not warrant a proof. |
| 證明留予恁練習 | | The proof is left as an exercise. |

* 推 tshui, thui
* 根 kin, kun, kirn
* 據 kì, kù, kìr
* 按呢 án-ne, án-ni
* 就 tiō, tō
* 袂 bē, buē