Question

Use the variable x to write the set in set-builder notation.

Let H be the set of integers less than one.

Answer 1

`\( H = \{ x \mid x < 1 \} \)` includes all integers for which
`\( x \)`is less than 1.

The set
`\( H \)` of integers less than one, denoted as
`\( \{ x \mid x < 1 \} \)`, can be expressed in set-builder notation using the variable
`\( x \)`. In this notation,
`\{\}` represents the set,
`\( x \)` is the variable, and
`\( x < 1 \)` provides the condition or property that elements in the set must satisfy.

So,
`\( H = \{ x \mid x < 1 \} \)` includes all integers for which
`\( x \)`is less than 1. This set encompasses values such as
`\( \dots, -3, -2, -1, 0 \)`, and extends indefinitely in the negative direction.

The set-builder notation succinctly conveys the rule or condition defining the elements of the set, making it a concise way to represent a collection of integers that meet the specified criteria.