Integers are a lot like the whole numbers that you already know. The main difference is that there are negative integers as well as positive integers. Zero is also an integer, but it is neither positive nor negative. Here is one way we can picture the set of integers:

As you can see, the negative integers are to the left of zero. We use a little minus sign to show that an integer is negative. Sometimes we use a little plus sign to show that an integer is positive, but we usually don't use any sign at all when the integer is positive.

Comparing integers

By looking at the number line we can easily tell which integers are greater (larger) than a certain number and which are less (smaller) than the number. When two numbers are located on a number line, the number to the right is larger than the number to the left.

–4 is less than –2 because it is to the left of –2. We write it like this "-4 < -2".

1 is greater than –2 because it is to the right of –2. We write it like this "1 > -2".

On a number line, the distance between the origin and the point that corresponds to the value of a number is called the absolute value of that number. For example, since the point corresponding to +3 is a distance of 3 from the origin, the absolute value of +3 is just 3. Likewise, since the point corresponding to -3 is a distance of 3 from the origin, the absolute value of -3 is also 3.

In general, the absolute value of a number is just equal to the number remaining after the positive or negative sign has been removed.

$\left|~-8\right|$ is read "the absolute value of negative 8". The value of $\left|~-8\right|$ is 8.

$\left|~-4\right|$ = 4 $\left|~+7\right|$ = 7

Self-Check

Q1: True or False. $\,\,\,\,\,-3\,>\,-5\,\,\,\,$ [show answer]

TRUE

Q2: Arrange these integers from least to greatest. $\,\,3,\,-2,\,-5,\,0\,\,\,\,\,$ [show answer]

$-5,-2,0,3$

Q3: Fill in the blank with <, >, or =. $\,\,-4\,[\,\,\,\,\,\,\,]\,0\,\,\,\,\,\,$ [show answer]