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I would like to know how to express mandatory conditions in Japanese. Since
Japanese distinguishes between different types of languages, I should probably
ask more precisely:

What is the right way to express equivalence statements (the kind a
mathematician might make) such as "The equation is satisfied if and only if
a>b"?

How do you express that you're going to do or that something will happen, only
if some condition is satisfied? ("I'll only go if you buy me an ice.", "The
plant will only grow if it is watered regularly.")
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2016-02-15T18:40:35.617
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2016-09-20T11:12:09.620
2016-02-15T18:52:27.750
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question
grammar conditionals mathematics
How do you say "if and only if" in Japanese?
* **if and only if** (= iff)

> a > b の **時、（そして／かつ）その時に限り** 等式が成立する。  
>  _The equation is satisfied **if and only if** a > b._

  * **only ... if**

    * ～なければ～ない (colloquially ～なきゃ～ない or ～なけりゃ～ない)  
≈ ～ないなら～ない

> アイスを買ってくれ **なきゃ** 行か **ない** 。  
>  _I'll **only** go **if** you buy me an ice._

    * ～ないと～ない

> この植物は定期的に水をやら **ないと** 育た **ない** 。  
>  _The plant will **only** grow **if** it is watered regularly._

    * The difference between them is, in short, you can't use the latter if your(= the speaker's) will intervenes.
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2016-02-15T19:09:57.110
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2016-02-15T19:43:40.463
2016-02-15T19:43:40.463
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answer
Two common ways of translating "if and only if" use the terms 必要十分条件
("necessary and sufficient condition") and 同値 ("equivalence").

> a > b は式 (15) である為の必要十分条件である。  
>  Equation (15) holds if and only if a > b.
>
> 式 （15） と「a>b」とは同値である。  
>  Equation (15) is equivalent to a > b.
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2016-02-15T19:23:57.263
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2016-02-15T19:23:57.263
2020-06-17T08:18:27.500
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answer