Final answer:
The set of all numbers greater than -8 and less than 1 is represented by the inequality -8 < x < 1, and includes all real numbers between -8 and 1, excluding the endpoints.
Step-by-step explanation:
The set of all numbers greater than -8 and less than 1 can be defined using inequality notation or interval notation. In inequality notation, this set is written as -8 < x < 1, meaning that x can be any number that is more than -8 but less than 1. In interval notation, this set is represented as (-8, 1), where the parentheses indicate that the endpoints -8 and 1 are not included in the set. This set includes all the real numbers that fall between -8 and 1, such as -7, -2, 0.5, and many others, including fractions and decimals within that range. It is important to note that the set is infinite and contains an uncountable number of elements.