Talk:Subband of Induced Operation is Set of Subbands

To my mind the separation between case 1 and 2 seems artificial. The problem here is grammar: "Let" has the connotation that whatever follows is definitely possible, while "Suppose" does not have that prerequisite. I have thought of this a few days back and it seems to hold up against everything I throw at it.

So if we replace the "Let" by "Suppose" in case 2, then it vacuously covers the case that $T$ is empty as well. — Lord_Farin (talk) 22:46, 7 March 2013 (UTC)

Is it worth writing the above insight (which I hadn't heard) into definition pages for "let" and "suppose"? --prime mover (talk) 23:22, 7 March 2013 (UTC)

As I brought it in, I'm not in a position to judge that. But it still seems like a sensible distinction. — Lord_Farin (talk) 23:35, 7 March 2013 (UTC)