Interval of a variable

Very often we confine ourselves to a portion only of the number system. For example, we may restrict our variable so that it shall take on only such values as lie between $a$ and $b$, where $a$ and $b$ may be included, or either or both excluded. We shall employ the symbol $\left \lbrack a,\ b \right \rbrack$, $a$ being less than $b$, to represent the numbers $a,\ b$, and all the numbers between them, unless otherwise stated. This symbol $\left \lbrack a,\ b \right \rbrack$ is read the interval from $a$ to $b$.