2013 (UTC)
 Hi Duxwing,
 Sorry for the very long response time.  The sentence "a Y such that Z exists for X" is much harder to decipher than the other version and because of the nontraditional order of quantifiers; in some cases it may have different meaning as a mathematical statement.  (It is also not noticably more concise.)  For example, the sentence "An element −v ∈ V for every v ∈ V exists" is impossible to parse because of the strange quantifier placement.  I suggest that if you are not familiar enough with higher mathematics to understand the importance of precision in quantifier choice and order then you should tread very carefully when editing technical phrases.  (Some of the other edits you made were unobjectionable or improvements, but they were all mixed in together and I didn't want to risk leaving an incorrect technical phrase.)
 All the best,  (talk) 02:09, 19 November