A double inequality is a specific type of compound inequality, written continuously in the form $a < x < b$. This concise mathematical notation represents two simultaneous conditions joined by the logical operator "and", meaning it is completely equivalent to stating that $a < x$ and $x < b$. Double inequalities can also use other combinations of strict and non-strict symbols, such as $a \leq x \leq b$, $a > x > b$, or $a \geq x \geq b$. Each of these continuous forms translates to an "and" relationship between the two boundaries, effectively describing a single, bounded interval on the number line.