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The number line is a fundamental tool in mathematics, primarily used for representing numbers and visualizing the relationship between them. Imagine a horizontal line that stretches infinitely in both directions. This line is divided into equal segments, each representing a number. The center of the line, typically labeled '0', is known as the origin. Numbers to the right of the origin are positive, while those to the left are negative.

When we place numbers on this line, we can easily compare their size. For instance, when comparing -100 and 0, you can see -100 positioned to the left of 0. This placement is not arbitrary—it reflects the relative value of numbers, indicating that -100 is less than 0. The number line is essential when working with integers, as it provides a visual cue for understanding which number is greater or lesser in value.

Integers include the whole numbers, which are the positive numbers (1, 2, 3, ...), zero (0), and the negative numbers (-1, -2, -3, ...). When comparing two integers, it's critical to understand their position in relation to each other on the number line. The further to the right an integer is on the number line, the greater its value, and vice versa.

For example, -100 and 0 are two points on the number line, with -100 found to the left of 0. This means that -100 is less than 0, as it is positioned further in the negative direction. Comparing integers is a basic yet vital skill, allowing you to quickly determine which number is larger or smaller and making it easier to perform operations such as addition and subtraction.

Mathematical inequalities are expressions that denote the relative size of two values. They are represented by symbols such as \(<\) (less than), \(>\) (greater than), \(\leq\) (less than or equal to), and \(\geq\) (greater than or equal to). The smallest value is always pointed to by the tip of the inequality symbol.

To use these symbols correctly, remember this simple rule: the symbol always 'eats' the larger number. So, in our exercise, since -100 is less than 0, we write \(-100 < 0\). Inequalities are not just for comparing numbers but are also crucial in algebra, where they help to express ranges and relationships between variables, and in calculus, where they describe the behaviors of functions and their graphs.