Define an integer.

An integer is a whole number that can be positive, negative, or zero, without any fractional part.

Integers are a fundamental concept in mathematics and are used in various calculations and problem-solving scenarios. They include numbers like -3, 0, 7, and 42. Unlike fractions or decimals, integers do not have a fractional or decimal component. This means that numbers like 1.5 or -2.75 are not considered integers.

Integers can be categorised into three main types: positive integers, negative integers, and zero. Positive integers are numbers greater than zero (e.g., 1, 2, 3), while negative integers are numbers less than zero (e.g., -1, -2, -3). Zero is a unique integer that is neither positive nor negative but serves as a neutral point on the number line.

In mathematical operations, integers follow specific rules. For example, when you add or subtract integers, you move along the number line. Adding a positive integer moves you to the right, while adding a negative integer moves you to the left. Multiplication and division of integers also follow particular rules, such as the product of two positive integers or two negative integers being positive, while the product of a positive and a negative integer is negative.

Understanding integers is crucial for solving equations, analysing data, and performing various mathematical tasks. They are the building blocks for more complex mathematical concepts and are widely used in everyday life, from counting objects to measuring temperature changes.