Should theorems, propositions, conjectures, etc. share a common counter?

Should theorems, proposition, conjectures, etc. share a common counter?

For example, is the following good, for a theorem and a proposition to share the same number?

Theorem 1. ...

Proposition 1. ...

What about sharing numbering for conjectures?

• It depends on the number of theorems and propositions, but in general I prefer shared numbering, so that it's easy to look for the statement. If each type has its own counter, will Proposition 3 be before or after Theorem 3? – egreg Sep 30 '12 at 16:40
• If you write 5 theorems and then 2 propositions and 2 more theorems and then refer to Proposition 2, it's a mess to find it. Shared counter approach doesn't suffer from this. Because it comes after from Object 1 and before Object 3 whatever the objects are. – percusse Sep 30 '12 at 16:55
• and of course, if the book is large, it is good to number them within chapter/section so that the number does not go large and you can find them more easily – yo' Sep 30 '12 at 17:00
• A reader seeing Theorem 3 could be tempted to think there were 2 theorems before that one. But no, there was Definition 1 and then Lemma 2. Maybe you should take your favorite author/editor couple and see how they do. – gniourf_gniourf Sep 30 '12 at 17:22
• Most of the time, the distinction between Proposition, Theorem, Lemma etc. is fairly arbitrary anyway. I don't think independent numbering makes sense. In particular, all of those will go into the list of theorems, won't they? So a shared numbering will give a canonical ordering here. Definitions and Examples are a different case, for which you will also have independent lists most of the time. – Stephan Lehmke Sep 30 '12 at 22:42