2.1+Integers

Section 2.1 - Integers

 * The Concept of Negative Amounts**

The idea of having a negative amount is somewhat challenging. It's hard to conceive of running a negative number of miles - even running backwards you would still be running a positive number of miles. But there are times when it makes sense. If you are running the football, but get tackled behind the line of scrimmage, it can be said that you lost three yards, or got "minus three yards". Either way, it is three yards less than you had before the play.


 * Opposites**

If you consider the numberline, the numbers count up from zero on the right side. But what do they do on the left side? They actually count down from zero on the left side, even though the digits seem to be going up. Negative five is less than negative three. It kind of looks like a mirror is placed at zero, with the positive and negative numbers matching up. Positive four and negative four are exactly four spaces away from zero, just in different directions. These numbers are considered to be "opposites" of each other. Positive four is the opposite of negative four, and negative four is the opposite of positive four.


 * The Set of Integers**

Earlier we said that the set of whole numbers started at zero and counted up -- one, two, three. ..


 * The set of numbers called integers includes all of the whole numbers, plus their opposites. ** You will see it written as I = { . . . -2, -1, 0, 1, 2, . . . } because it goes on forever in both positive and negative directions. These numbers are also often called signed numbers because they have a positive or negative sign attached to them, even if we don't usually write the plus sign for a positive number.

Look at the numberline carefully and see that this simple rule always applies:** If you have two numbers, the one to the right on the numberline will always be greater **(have a higher value).



The symbols **<** and **>** are used to represent a comparison between the value of numbers. The wide end of the symbol points to the greater value, while the pointed end points to the lesser value. 9 > - 4 means that 9 is greater than - 4. It doesn't matter which symbol you use, (it is the same symbol just turned around), or which side the numbers are on, as long as the statement is true. So, 9 > - 4 could also be written as ( - 4 ) < 9.

This numberline shows that it doesn't matter if both number are positive, both are negative, or they have different signs, the number to the right is always greater. The tricky part is that negative nine is less than negative 4, even though 9 is more than 4. In this case, the higher digit (9), simply means that it is even "more negative", or of even less value.

**Where to from here?**
2.1 Integers 2.2 Absolute Value 2.3 Adding Integers 2.4 Subtracting Integers 2.5 Multiplying Integers 2.6 Dividing Integers 2.7 Exponents and Roots Chapter Two Summary Chapter Two Homework