Interval : An interval is a part of the number line between two numbers $a$ and $b.$ $a$ and $b$ can but do not have to be part of the interval. If $a$ and $b$ are part of the interval the interval is a closed interval. If $a$ and $b$ are not part fo the interval the interval is an open interval. If either $a$ or $b$ but not both are part of the interval the interval is called half-open or half-closed. $a$ can be equal to $-\infty$ and $b$ can be equal to $\infty$.