# Is 0<d,l<1 equivalent to writing separately 0<d<1 and 0<l<1 ?

1. ### FortzaParis

3
Is "0<d,l<1" equivalent to writing separately "0<d<1" and "0<l<1"?

Dear all, I'm writing a paper for a scientific journal and I need to save as much typographic space as I can. In a proposition, I need to specify that the parameters "d" and "l" assume values between zero and one. I am wondering if (in scientific writing) is it correct to write "0<d,l<1", instead of writing separately "0<d<1" and "0<l<1". Thanks!

2. ### Mentallic

3,648
I've been using the shorthand form like that for years now, and no professors of mine have ever complained about it. In fact, from my recollection, I've seen some professors use the short form while others don't.

The way I see it, if it is clear to the reader and doesn't need moments to be deciphered, it's good enough to use.

3. ### FortzaParis

3
Thanks, Mentallic!

4. ### disregardthat

1,811
I would personally interpret that as 0<d and l<1, but I don't know if this is common. The comma seems to separate the two statements "0<d" and "l<1".

What about $$d,l \in (0,1)$$?

5. ### HallsofIvy

40,212
Staff Emeritus
I also would tend to interpret "0< d,l< 1" as "0< d< 1" and "0< l< 1" or "both d and l are between 0 and 1". If you mean 0< d and l< 1, grammatically, you should have the word "and" between them, not a comma.

6. ### disregardthat

1,811
How would one interpret the sentence "0<d, l<1 and p>3"?

This is probably an insignificant issue, but grammatically commas are used to separate things.

7. ### 1MileCrash

I tend to agree with HOI here, but the context does matter. If this was part of a statement that disregardthat proposes, I would lean the other way.

But if there was no listing of relations, and the comma appeared instead of an and, there would be no reason to write something that way unless you meant what the OP intended.

8. ### micromass

18,440
Staff Emeritus
I often write ##0<d,l<1## to mean ##0<d<1## and ##0<l<1##. I've also seen it in a lot of mathematical texts, so I guess it's standard.

9. ### Anonomouse

1
I agree with micromass, it (or in equivalent circumstances) is used regularly in school level maths

10. ### FortzaParis

3
Dear all, thanks for the suggestions! I think I will write $$d,l \in (0,1)$$ so that there is no possibility of misunderstanding.

11. ### Mentallic

3,648
Personally, the reason I wouldn't interpret it like that is because it would be a very odd way to do it.
0<d,l<1 is a quite commonly used expression, while it's very uncommon to put the variable of an unbounded inequality on the right side. 0<d would most often than not be d>0.