0

Good evening,

I have a small question: I am currently writing my master's thesis in mathematics, and I have a lot of equations full of estimates like $\|\cdots\|_1 \leq C \|\cdots\|_2$ where some constants get involved, which are ultimately meaningless, since its just about having an estimate for the norms.

Instead of introducing numerous constants like $C_1, C_2, ...$, I have seen some papers/ scripts always use the same letter and write something like "with the constant $C$ possibly changing". Although I think this is sometimes bad for understanding certain steps, I wonder if I should implement this...

So, my question boils down to: Is something like this considered bad style or sloppy writing?

Nuke_Gunray
  • 2,816
  • 1
    If the value of the constant really doesn't matter and you can keep what it depends on straight during the calculation, then this is pretty standard practice. – Ian Jun 29 '22 at 16:25
  • 1
    No, it's very standard – mathworker21 Jun 29 '22 at 16:33
  • 2
    Using the same letter for arbitrary, not-necessarily-equal constants is not unusual. Of course, if you're mixing them in a single formula, then you'll probably need to give them distinguishing letters or subscripts or whatever. ... That said, you should bring this issue to your thesis advisor. They'll be able to provide specific guidance, perhaps with helpful alternatives, based on the full context of your work. – Blue Jun 29 '22 at 16:39
  • 2
    You could introduce a term e.g. "we will say $f$ is $g$-bounded if some constant $C$ satisfies $\Vert f\Vert_1\le C\Vert g\Vert_2$". You can then probably show fewer equations, especially outside the proofs of suitable helper theorems. – J.G. Jun 29 '22 at 18:12

0 Answers0