I'm reading a mathematics textbook, and there are a number of sentences which end with もの or こと.
I can work out the intended meaning no problem, so what I would like explained to me, are the rules for when I can use this grammatical construction.
This seems to happen in definitions, especially if mathematically written conditions are involved.
m1, m2 ∈ N ⇒ m1 + m2 ∈ N, さらに 0 ∈ N
r ∈ R, n ∈ N ⇒ r•n ∈ N
f: S → T 全射 (surjection, epimorphism) であるとは、f (S) = T が成立すること。
I asked a (non-Japanese) mathematician, who told me that this can be used to give commands, e.g., 勉強すること。However, I don't see why a command would appear in definitions in this way...