To represent all the real numbers between two specific numbers we use intervals. They can be open or closed intervals, depending if we want or not to include the "endpoints". For example, the interval $(2,5)$ represents all numbers $x$ such that $2 < x < 5$ (note the inequality is strict). Similarly, we have: $$\begin{aligned}(2,5) &= \{x \mid 2 < x < 5\} \\ [2,5] &= \{x \mid 2\leq x \leq 5\} \\ (2,5] &= \{x \mid 2 < x \leq 5\} \\ [2,5) &= \{x \mid 2\leq x < 5\}. \\ \end{aligned}$$

Sometimes, however, we want to represent all numbers that are greater than or smaller than a given number. In some way, this means there is no left endpoint or right endpoint. That is when we use $\infty$ together with interval notation. For example, the interval $(10,\infty)$ represents all numbers $x$ such that $10 < x $ (note there is no right "endpoint"). Similarly, we have: $$\begin{aligned} (-\infty,10) &= \{x \mid x < 10 \} \\  (-\infty,10] &= \{x \mid x \leq 10 \} \\ (10,\infty) &= \{x \mid 10 < x \} \\ [10,\infty) &= \{x \mid 10 \leq x \}. \\ \end{aligned}$$