91Ó°ÊÓ

Set notation is a way to define a collection of elements. Sets can include numbers, objects, or even other sets. We use braces \{ \} to enclose the elements of a set. For example, \{1, 2, 3\} is a set with the elements 1, 2, and 3.
A set can also be defined by a property that its members must satisfy. This is done using a vertical bar \| which stands for 'such that.'
In the given exercise, \( \{ p \,|\, p \text{ is an integer less than } 3 \} \), the set includes all integers \( p \) that satisfy the condition of being less than 3.
When we write a set using such a property, we call it 'set-builder notation.' This form helps to clearly define the set without listing all the elements, which is useful for very large or infinite sets.

Integers are a set of numbers that include all positive whole numbers, negative whole numbers, and zero. They are denoted as \( \mathbb{Z} \).
Some examples of integers are -3, -2, -1, 0, 1, 2, and 3. These numbers do not have any fractional or decimal parts.
In the given problem, we are asked to list integers less than 3. So, we include all negative whole numbers, zero, and positive whole numbers that meet the condition.
The official list of integers less than 3 is \( ..., -3, -2, -1, 0, 1, 2 \). This is an infinite set because there is no lower limit on the negative integers.

Inequalities in algebra are statements about the relative size or order of two elements. Common inequality symbols include:

• \(<\) for 'less than'
• \(>\) for 'greater than'
• \(\leq\) for 'less than or equal to'
• \(\geq\) for 'greater than or equal to'

In our exercise, the inequality \(p \text{ is an integer less than } 3\) is represented as \( p < 3 \). This means we include all integers that are smaller than 3.
To solve inequalities, you must determine which values satisfy the condition. For example, with \( p < 3 \), you list integers starting from the largest number less than 3 (which is 2) and work downwards to include all possible values.