Is the closed interval [3,0] an empty set?

Question

For example [0,3] would be all the numbers from 0 to 3 inclusive. However, would this still hold if it was [3,0].

Answer 1

In some books $[a,b]$ is defined explicitly assuming $a \le b$. If your text uses a different convention, I suppose it would have to be spelled out.

Assuming a "default" notion that $[a,b]$ denotes all real numbers at least $a$ and at most $b$, you will be hard-pressed to find a real number $x$ with $0 \ge x \ge 3$...