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so that
From dictionary.com
- In order that, as in I stopped so that you could catch up.
- With the result or consequence that, as in Mail the package now so that it will arrive on time.
- so ... that. In such a way or to such an extent that, as in The line was so long that I could scarcely find the end of it.
All three usages date from a.d. 1000 or earlier, and the first two are sometimes put simply as so, as in
I stopped so you could catch up, or
Mail it now so it will arrive on time. Source: The American Heritageｮ Dictionary of Idioms by Christine Ammer.
Copyright ｩ 1997 by The Christine Ammer 1992 Trust. Published by Houghton Mifflin Company
such that
From mathworld.wolfram.comA condition used in the definition of a mathematical object. For example, the rationals can be defined as "the set of all m/n such that n is nonzero and m and n are integers ." From dictionary.com
- adj : of a degree or quality specified (by the `that' clause); their anxiety was such that they could not sleep
Source: WordNet ｮ 2.0, ｩ 2003 Princeton University
Examples
- Take x to be a real number so that x2 is non-negative. [Correct]
- Take x to be a real number so that x2+1 is greater than 4. [Incorrect]
- Take x to be a real number such that x2+1 is greater than 4. [Correct]
- The subset H of the Lie group G is a discrete subgroup so that G/H is compact. [Incorrect --- not all discrete subgroups of Lie groups have compact quotient; this is from the Annals of Math., 107, p313.]
Briefly, if omitting the "that" from "so that" renders the sentence nonsense, then you should probably have used "such that".
You won't find "so that" among lists of commonly misused phrases because only mathematicians commonly misuse it. Probably the error arose from the influence of German, where the two are not distinguished.