Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

In definitions and exercises, I notice that "so that" and "such that" are seemingly used interchangeably. Are they in fact interchangeable, or is one more appropriate for a specific context?

Note: $\mathrm{Dom}\,(f)$ means the domain of $f$.

Example 1:

Suppose that a function $f$ is continuous at a point $c$ and $f(c) > 0$. Prove that there is a $\delta > 0$ $\color{red}{\text{so that}}$ for all $x \in \mathrm{Dom}\,(f)$, $$ |x-c| \le \delta \ \Rightarrow \ f(x) \ge \frac{f(c)}{2} $$

Example 2:

A function $f(x)$ is continuous at a point $c \in \mathrm{Dom}\,(f)$ if and only if for each $\varepsilon > 0$ there is a $\delta > 0$ $\color{red}{\text{such that}}$ for all $x \in \mathrm{Dom}\,(f)$: $$ |x - c| \le \delta \ \Rightarrow \ |f(x) - f(c)| \le \varepsilon $$

share|cite|improve this question
To me in this case “such that” seems more appropriate. “So that” to me is to be used when something is to be constructed or demonstrated to have a property, while “such that” means that we assume a property of an object. But I'm not a native English speaker, so I might be wrong. :) – tomasz Aug 16 '12 at 19:05
19 – Andrew Aug 16 '12 at 19:05
@Andrew: a very nice link, thank you! :) – tomasz Aug 16 '12 at 19:07
Agreed, thank you @Andrew – Moderat Aug 16 '12 at 19:08
@David: I’ve answered some questions there; based on my experience, it would probably be suggested that this question would be better asked here. – Brian M. Scott Aug 16 '12 at 19:35
up vote 4 down vote accepted

Seeing as no one has posted their response as an answer, I simply don't want this to come up under "Unanswered Questions." For the actual answer to this question, consider the comments.

share|cite|improve this answer
You can also accept it, if you want. – M Turgeon Aug 18 '12 at 18:46
Sorry about that, I left my computer and hadn't come back to accept it yet because when I posted that it said I had to wait 45 minutes – Moderat Aug 18 '12 at 19:40

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.