Student: What exactly is an integer?

Mentor: Well, you know what the natural numbers are, right?

Student: Yes, the natural numbers are the counting numbers, 1, 2, 3, 4, 5, and so on.

Mentor: That's right. The integers are a set of numbers including the natural numbers as well as zero and the negative numbers.

Student: The negative numbers?

Mentor: Yes, the negative numbers are the opposite of the natural numbers, also called positive numbers, and are usually expressed as -x (if x is a natural number). Think about it like this: if the number 5 is greater than zero by five units, then -5 is less than zero by five units.

Student: So that means that a positive number is always greater than its negative.

Mentor: Exactly, and furthermore it means that any positive number is greater than any negative number. It is also interesting to note that as a positive number gets larger its negative counterpart gets smaller.

Student: Then that means -8 is less than -3 since 8 is greater than 3.

Mentor: It seems like you understand. Now, can you think of a situation where you would use negative numbers?

Student: Wouldn't you use negative numbers if, for instance, you owed more money than you had in your account. If you were in debt $300, then the amount of money you have could be represented as -$300.

Mentor: That's good, but can you think up one more example just to be certain you understand.

Student: Yes, in golf negative numbers are used to describe how many strokes a player is below par. For instance, if you were 5 strokes below par, your score could be expressed as -5, or "five under par".