正式的用語

1. definition (定義)
• 符號的意義，通常用來描述某種數學語法，像是 $\lim , \sum, \int, ...$]
2. axiom (公理)
• 假定,公設 — 作為自明之理，在歐氏幾何原本中使用 postulate 也是這個意思。
3. proposition (命題)
• 一個等待證明的假設或算式，一但證明完畢就成為定理 (Theorem)
4. corollary
• a proposition inferred immediately from a proved proposition with little or no additional proof
5. lemma (引理)
• an auxiliary proposition used in the demonstration of another proposition
6. theorem (定理)
• a formula, proposition, or statement in mathematics or logic deduced or to be deduced from other formulas or propositions

有趣的說法

Phrases often have different meanings in mathematics than in everyday usage. Here I have collected definitions of some mathematical terms which might confuse the novice.

1. beyond the scope of this text
• Beyond the comprehension of the author.
2. difficult
• Essentially impossible. Note that mathematicians never refer to problems they have solved as being difficult.
• This would either be boastful, (claiming that you can solve difficult problems), or self-deprecating, (admitting that you found the problem to be difficult).
3. interesting
• This word is grossly overused in math and science. It is often used to describe any work that the author has done, regardless of the work’s significance or novelty. It may also be used as a synonym for difficult. It has a completely different meaning when used by the non-mathematician. When I tell people that I am a mathematician they typically respond with, “That must be interesting.”, which means, “I don’t know anything about math or what mathematicians do.” I typically answer, “No. Not really.”
4. non-obvious or non-trivial
• Real fuckin’ hard.
5. one can prove that … :
• The “one” that proved it was a genius like Gauss. The phrase literally means “you haven’t got a chance in hell of proving that … ”
6. simple:
• Mathematicians communicate their prowess to colleagues and students by referring to all problems as simple or trivial. If you ever become a math professor, introduce every example as being “really quite trivial.”

本文改寫自

1. Unabridged Version of Sean's Applied Math Book (No rights reserved)