One of my mathematics teachers, a long time ago, once objected to statements of the type
Let X and Y be two compact topological spaces. Then X x Y is also compact
on the ground that the use of two implied that the statement did not apply to the case of X x X, whose compacity would need to be stated separately, as it was not, strictly speaking, an application of the given statement.
His favored solution was to drop the two (or, in French, to replace Soient X et Y deux espaces… by Soient X et Y des espaces….), with the idea (I presume) that making a grammatical mistake (using a plural form like des when, sometimes, there is only one object, if X=Y) would be less important than a mathematical one.
Strangely enough, I still sometimes remember this, and I have modified various sentences to try to go around it, although the whole thing seems quite absurd really… I wonder if others have heard this type of rules, and if there’s a mathematically and syntaxically correct way to phrase things without being absurdly formal?
