Open versus closed intervals

What’s the difference between open and closed intervals?

Related to notes/ Range — the difference between maximum and minimum values of a sequence.

Closed intervals #

The notation for closed intervals is [start, end]. In closed intervals, the endpoints are included.

For example $[-2, 2]$ represents all values from $-2$ to $2$, including $-2$ and $2$. It can also be written as $-2 \leq x \leq 2$.

Open intervals #

The notation for open intervals is (start, end). In open intervals the endpoints are excluded.

For example, $(-2, 2)$ represents all values between $-2$ and $2$, but not including $-2$ and $2$. It can also be written as $-2 \lt x \lt 2$.

Mixing open and close interval notation #

• $[-2, 2)$: includes $-2$, excludes $2$
• $(-2, 2]$: excludes $-2$, includes $2$