How to interpret 2 variables separated by a comma in chained inequalities

What does $0\le x,y\le1$ mean? See the red circled part in the image below for an example.

1. I first thought it meant: $x\ge0$ and $y\le1$

2. Then I thought it meant: $0\le x\le y \le 1 $

3. But, based on the green part, I believe it means: $x$ and $y$ are in $[0,1]$

Is this notation unambiguous? In probability, the comma means $\bigcap$, so, to me, these are "separate" statements, as in (1) and not (3).

Solution 1:

I would take it as c, that both $x$ and $y$ are between $0$ and $1$ and think that it should be unambiguous. I might have a worry in my stomach that it was $a$ and be alert to the possibility as I read on or check back to make sure. I would say b is wrong and should be written the way you did.

Solution 2:

It is a convention for $0\leq x \leq 1$ and $0 \leq y \leq 1$ and is mostly to avoid typing it out twice. The comma is used this way in the equivalent statement $x,y \in [0,1]$ as well so it's consistent with that notation.