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The number 0 is neither positive nor negative.
The set of real numbers has many subsets. Some of the subsets that are of interest in the study of algebra are listed below along with their notations and graphs.
Notice that every natural number is a whole number.
Notice that every whole number is an integer.
Some rational numbers are graphed below.
Notice that every integer is a rational number .
Notice that there are still a great many points on the number line that have not yet been assigned a type of number. We will not examine these other types of numbers in this text. They are examined in detail in algebra. An example of these numbers is the number , whose decimal representation does not terminate nor contain a repeating block of digits. An approximation for is 3.14.
Is every whole number a natural number?
No. The number 0 is a whole number but it is not a natural number.
Is there an integer that is not a natural number?
Yes. Some examples are 0, -1, -2, -3, and -4.
Is there an integer that is a whole number?
Yes. In fact, every whole number is an integer.
If we let and represent two numbers, then and are related in exactly one of three ways: Either
What integers can replace so that the following statement is true?
The integers are -3, -2, -1, 0, 1.
Draw a number line that extends from -3 to 5. Place points at all whole numbers between and including -1 and 3.
-1 is not a whole number
What integers can replace so that the following statement is true?
-5, -4, -3, -2, -1, 0
Draw a number line that extends from -4 to 3. Place points at all natural numbers between, but not including, -2 to 2.
For the following 8problems, next to each real number, note all collections to which it belongs by writing for natural number, for whole number, or for integer. Some numbers may belong to more than one collection.
Is the number 0 a positive number, a negative number, neither, or both?
Neither
An integer is an even integer if it is evenly divisible by 2. Draw a number line that extends from -5 to 5 and place points at all negative even integers and all positive odd integers.
Draw a number line that extends from -5 to 5. Place points at all integers that satisfy .
Is there a largest two digit number? If so, what is it?
Is there a smallest two digit number? If so, what is it?
Yes, 10
For the pairs of real numbers in the following 5 problems, write the appropriate symbol (<,>, =) in place of the □.
For the following 5 problems, what numbers can replace m so that the following statements are true?
, an integer.
, a natural number.
For the following 10 problems, on the number line, how many units are there between the given pair of numbers?
Are all positive numbers greater than all negative numbers?
Is there a largest natural number?
( [link] ) Convert to an improper fraction.
( [link] ) Find the sum of .
( [link] ) Find the area of the triangle.
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