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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 $x \in \mathrm{Dom}\,(f)$: $$ |x - c| \le \delta \ \Rightarrow \ |f(x) - f(c)| \le \varepsilon $$

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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
jmilne.org/math/words.html –  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 –  KingOliver 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

1 Answer 1

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.

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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 –  KingOliver Aug 18 '12 at 19:40

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