Given the set notation [tex]\(\{x \mid -1 \leq x \}\)[/tex], we want to express it in interval notation. Let's break down the set notation step-by-step:
1. Understand the set notation: The given set is [tex]\(\{x \mid -1 \leq x \}\)[/tex], which reads as "the set of all [tex]\(x\)[/tex] such that [tex]\(-1\)[/tex] is less than or equal to [tex]\(x\)[/tex]".
2. Identify the bounds:
- The smallest value that [tex]\(x\)[/tex] can take is [tex]\(-1\)[/tex], and this value is included in the set (as indicated by the 'less than or equal to' [tex]\( \leq \)[/tex]).
- There is no upper bound specified for [tex]\(x\)[/tex]; [tex]\(x\)[/tex] can be any value greater than or equal to [tex]\(-1\)[/tex].
3. Convert to interval notation:
- Since [tex]\(x\)[/tex] can take any value starting from [tex]\(-1\)[/tex] and going upwards, we use [tex]\(-1\)[/tex] as the lower bound, and since there is no upper limit, we use [tex]\(\infty\)[/tex].
- The interval notation includes [tex]\(-1\)[/tex] in the set, so we use a square bracket [tex]\([ \)[/tex] to denote that [tex]\(-1\)[/tex] is included.
- Infinity ([tex]\(\infty\)[/tex]) is always used with a parenthesis [tex]\(()\)[/tex] in interval notation because infinity is not a finite number and cannot be included in a closed interval.
Therefore, combining these elements, the interval notation for the set [tex]\(\{x \mid-1 \leq x\}\)[/tex] is [tex]\(\boxed{[-1, \infty)}\)[/tex].
