"so that" vs "such that"

So that or such that? Found a nice article that covers these issues, as well as a few other cool grammar bits for mathematicians.

From the article:

Here are the definitions.

so that

1. In order that, as in I stopped so that you could catch up.
2. With the result or consequence that, as in Mail the package now so that it will arrive on time.
3. 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.

From dictionary.com

such that

1. adj : of a degree or quality specified (by the "that" clause); their anxiety was such that they could not sleep. (dictionary.com)
2. A 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 . (mathworld.wolfram.com)

Examples

1. We require x to be a rational number so that mx is an integer for some m. [Correct]
2. We require x to be a rational number so that 3x is an integer. [Incorrect; should be such that 3x is an integer.]
3. Let H be a discrete subgroup of the Lie group G 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.]
4. Let N and N' be submodules of a module M such that N contains N', so that N/N' is a submodule of M/N'. [Correct! From Steps in Commutative Algebra.]

Briefly, if omitting the "that" from "so that" renders the sentence nonsense, then it was already nonsense, and you should have used "such that". You won't find "so that" among lists of commonly misused expressions because only mathematicians commonly misuse it. Probably the error arose from the influence of German on American (mathematical) English, since the two are not distinguished in German.

Mathlish