Exploring Negative Integers

In your math journey so far, you've mostly used whole numbers starting from $0$. But sometimes, we need to go below zero. Integers are the set of whole numbers and their opposites. This includes positive numbers ($1, 2, 3...$), negative numbers ($-1, -2, -3...$), and zero. Zero is special because it is neither positive nor negative—it is the 'neutral' starting point. We use negative numbers to describe things like being in debt, temperatures below freezing, or depths below sea level.

A number line is like a map for integers. On a horizontal line, positive numbers live to the right of zero, and negative numbers live to the left. On a vertical line (like a thermometer), positives are above zero and negatives are below. The further a number is to the right (or higher up), the larger it is. Even though $10$ is bigger than $5$, $-10$ is actually smaller than $-5$ because it is further away from zero in the negative direction.

To compare integers, we use inequality symbols: $>$ (greater than) and $<$ (less than). A helpful trick is to remember that the symbol always 'eats' the larger number. On a number line, any number to the right is always greater than any number to its left. This means that any positive number is greater than any negative number. For example, $1 > -100$ because $1$ is to the right of $-100$.