I was told that such that and for which are not interchangeable, but I cannot determine which one to use. For example,
(a) The collection of numbers x for which x is even.
Or
(b) The collection of all numbers x such that x is even.
I would probably go with (b) instead of (a), but I am not sure why. There are times when for which seems more appropriate, such as the following.
There are subsets of R for which the amount of time the orbit spends in those open sets is not proportional to the sizes of the
sets.
When should I use such that or for which and when are they interchangeable?
Best Answer
The reason that (a) sounds odd is that the antecedent of "which" must be "collection," but the closest available noun is "x." What (a) means is
This refers to a property of the collection. Unfortunately, the proximity of "x" distracts the reader into thinking the property is about "x." Note that your second example excites no discomfort because you're talking about a property of some subsets of R.
The locution
is merely shorthand for "those x with property P," so the phrase "such that" is properly placed.