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Chapter 2—Integers

2-1 Introducing Integers

 When you complete the work for this section, you should be able to: Describe how the integer number system is different from the whole number system. Sketch and explain how to interpret the integer number line. Describe how plus and minus signs are used for indicating whether an integer has a positive or negative value.

The set of whole numbers (or natural numbers) consists of the customary counting numbers such as 1, 2, 3, 4, 5 and so on. The whole-number system begins with zero and runs endlessly upward toward infinity. When counting backwards, however, the whole-number system ends at zero.

But being able to count from 0 up to infinity isn't enough to satisfy the mathematical needs of modern commerce and technology.  There is a larger set of numbers known as integers. Like whole numbers, integers are numbers that are used for counting and specifying exactly "how many."  The set of integers, however, also allows us to count backward through 0 and toward infinity in the negative direction.

The number line for integer values includes:
• All the positive whole numbers
• Zero
• All the negative whole numbers Number line for the set of integers.

 Counting up and down with integers

Negative-value integers are located to the left of the zero on the integer number line. Negative-value integers use the same symbols as the whole number system, but are distinguished by the use of a negative sign  ( – ).  Numbers 5 and – 5, for example, might resemble one another in most respects, but they are two entirely different values. Refer to the integer number line shown here, and you will see that 5 and – 5 are located in two entirely different places.

Positive-value integers are located to the right of the zero on the integer number line. Positive integers are sometimes indicated with a positive sign ( + ). More often, however, we omit the positive sign. So when you see an integer value that does not have a sign, you can rightly assume it is a positive value.

Suppose you are playing countdown to blastoff: five, four, three, two, one, ZERO! But then you would like to keep going. How can we count backward past zero? That's easy—use negative numbers. Like this: five, four, three, two, one, zero, minus-1, minus-2, minus-3, and so on. You can count the "minuses" all the way to minus-infinity.

 Note A plus sign (+) is used for two entirely different purposes: to indicate the addition operation to indicate a positive integer value. Likewise, a minus sign ( – ) is used for two entirely different purposes: to indicate the subtraction operation to indicate a negative integer value. This can be confusing at times, but we all have to learn to live with the double meanings of the + and – signs. Zero (0) has no sign.

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