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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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    Thank you @MarkDominus, "terminology" is a more appropriate tag2012-08-16
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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. :)2012-08-16
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    http://www.jmilne.org/math/words.html2012-08-16
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    @Andrew: a very nice link, thank you! :)2012-08-16
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    Agreed, thank you @Andrew2012-08-16
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    There is an English stack exchange site. Perhaps that would be a better fit to this question.2012-08-16
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    I thought about that @DavidMitra but then I considered that mathematicians were the most accustomed to the "pidgin English" (to quote Andrew's source) that mathematics is written in.2012-08-16
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    @David: I’ve answered some questions there; based on my experience, it would probably be suggested that this question would be better asked here.2012-08-16
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    @Andrew: the link is indeed nice, but its author unfortunately blunders by arguing that "$a(n)\neq0$ for all $n$" should mean "some $a(n)$ is nonzero" instead of "all $a(n)$ are nonzero", which is ridiculous.2012-08-16
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    Dear @MarcvanLeeuwen, I hadn't actually looked that far when I posted the link. But, I think his point is that the statement is ambiguous. Does it mean that $a(n)$ is never zero, or that $a(n)$ is not *always* zero?2012-08-16
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    Dear @Andrew: In my view there is no ambiguity: formulas _always_ bind more tightly than text, so the "for all $n$" can only apply to all of "$a(n)\neq0$". Assuming that, as Milne suggests, one could take the negation bar out of the formula and make it say "NOT ($a(n)=0$ for all $n$)" is what I consider ridiculous. Note that one can't even do this is you pronounce "$\neq$" as "is unequal to".2012-08-16

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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.2012-08-18
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    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 minutes2012-08-18