"in or on" the interval

Do we say “in the interval (infinity, 3)” or “on the interval (infinity, 3)”?

In the interval

Until now I have the doubt how to use: in, on, at…
Can you explain?

In other areas it would be “in the interval”, but in maths “on the interval” is quite commonly used, possibly depending on exact context.

Incidentally, wouldn’t it be the interval (3, infinity) rather than (infinity, 3)?

Thanks, Mister Micawber.

Erm…, do you mean something such as the following examples?

  1. Solve for x by finding all values in the interval (0 , 2pi) inclusively that…
  2. Show that f is increasing on the interval (3, infinity)…

Oh My Goddess! What did I type in here? It should be (3, infinity), of course …