It seems you're referring to three different intervals: $[0, -1]$, $[1, \infty)$, and $[-1, 0]$. Let me clarify each:

1. $[0, -1]$: This is likely intended to be written as $[-1, 0]$, which represents the interval of all real numbers from -1 to 0, inclusive. In standard interval notation, $[a, b]$ requires $a \leq b$. Therefore, $[0, -1]$ doesn't typically make sense unless you're switching bounds, in which case it's really $[-1, 0]$.

2. $[1, \infty)$: This represents all real numbers greater than or equal to 1 and continuing infinitely. The bracket around 1 means 1 is included in the interval, and the parenthesis around infinity means that infinity itself is not included (because infinity is not a number but a concept).

3. $[-1, 0]$: This interval includes all real numbers from -1 to 0, inclusive of both endpoints. It is the same as the corrected version of your first interval.

If you're looking for operations involving these intervals (like union, intersection, or some specific function on them), let me know!

Would you like further details or explanations on any of these intervals? Here are five related questions:

1. How do you determine the union or intersection of intervals?
2. Can intervals represent domains and ranges of functions?
3. What is the difference between open and closed intervals?
4. How do you find the complement of an interval on the real line?
5. How do intervals relate to inequalities?

Tip: When working with intervals, always check if they are open (parentheses) or closed (brackets) to ensure you understand which endpoints are included.