In mathematical texts, but not only there, one often first names an object and then explains what it is in a “where” clause, for example:
“Let x and y be any two numbers from a set M of natural numbers, where M is given by the following property ...”
Is such a construction acceptable? Are there better choices instead of “where” for the same overall structure?
Clearly, overly long sentences are to be avoided. Whenever possible, one should try to decouple the two definitions. Here an alternative would be to first introduce M and then talk about x and y, but if we are mainly interested in x and y, first digressing to M feels like disrupting the flow of the text.
Simply splitting the above into two sentences creates, in my humble opinion, the impression that M should be known already, causing the reader to look back for its definition.