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Understanding inequality symbols is essential in precalculus and mathematics as a whole. These symbols serve as a shorthand to compare the size or order of numbers. The most common inequalities are '<' (less than), '>' (greater than), '≤' (less than or equal to), '≥' (greater than or equal to), '≠' (not equal to), and '=' (equal to).

In the context of the exercise, the symbol '≥' signifies that the number on the left side of the inequality, which is 0 in this case, is either greater than or equal to the number on the right side, which is -13. It's crucial to know that with '≥' or '≤', equality is included. So, if the two numbers are the same, the statement would also hold true. Inequalities are foundational in mathematics for defining the range of possible solutions to equations and for expressing the relationships between variables.

Comparing numbers is a fundamental skill in mathematics, allowing us to understand the relative value of numbers. To determine which of two numbers is greater or lesser, we need to look at their values on the number line. Positive numbers are always greater than negative numbers, and as we move to the right on the number line, the value of the numbers increases.

Comparing 0 to -13, we can easily see that 0 is to the right of -13 on the number line, which makes 0 greater than -13. By understanding these principles, the solution to exercises involving comparisons becomes more intuitive. Additionally, the comparison of numbers is not limited to integers; it applies to all types of real numbers, including fractions, decimals, and irrational numbers.

Number properties are the rules that numbers follow and are critical to understanding the correct way to manipulate and compare them. Some of the most fundamental number properties are the Commutative, Associative, and Distributive properties. These apply to addition and multiplication but not to subtraction and division.

In the case of inequalities, the properties of the numbers play a role in simplifying expressions and solving equations. For example, when dealing with inequalities, it's important to remember that if you multiply or divide both sides of an inequality by a negative number, the direction of the inequality changes. Knowing and applying the correct number properties saves time and helps avoid errors in mathematical reasoning and computation.