1. The phrase "between... and..." in mathematics usually describes an interval or range of numbers. 2. Whether or not you include the first and last numbers depends on the context or specific wording: - If the phrase is "between $a$ and $b$", it often means the numbers greater than $a$ and less than $b$, excluding $a$ and $b$ themselves. This is called an open interval, written as $$ (a,b) = \{x : a < x < b\} $$. - If the phrase is "between $a$ and $b$ inclusive", it means you include $a$ and $b$ as possible values. This is a closed interval, written as $$ [a,b] = \{x : a \leq x \leq b\} $$. 3. To summarize, pay attention to words like "inclusive" or symbols such as brackets: - Round parentheses $($ $)$ mean exclude endpoints. - Square brackets $[ ]$ mean include endpoints.