ReAl NuMBeRs

Category: Education

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INTRODUCTION The real number system evolved over time by expanding the notion of what we mean by the word “number.” At first, “number” meant something you could count, like how many sheep a farmer owns. These are called the natural numbers, or sometimes the counting numbers.


NATURAL NUMBERS 1, 2, 3, 4, 5, . . . The use of three dots at the end of the list is a common mathematical notation to indicate that the list keeps going forever. At some point, the idea of “zero” came to be considered as a number. If the farmer does not have any sheep, then the number of sheep that the farmer owns is zero. We call the set of natural numbers plus the number zero the whole numbers.


WHOLE NUMBERS Natural Numbers together with “zero” 0, 1, 2, 3, 4, 5, . . .


INTEGERS Whole numbers plus negatives . . . –4, –3, –2, –1, 0, 1, 2, 3, 4, . . .


RATIONAL NUMBERS All numbers of the form , where a and b are integers (but b cannot be zero) Rational numbers include what we usually call fractions Notice that the word “rational” contains the word “ratio,” which should remind you of fractions.


IRRATIONAL NUMBERS Cannot be expressed as a ratio of integers. As decimals they never repeat or terminate (rationals always do one or the other)

Diagram: : 

Diagram: The following diagram illustrates the relationships of the sets that make up the real numbers.

The Number Line: : 

The Number Line: The ordered nature of the real numbers lets us arrange them along a line (imagine that the line is made up of an infinite number of points all packed so closely together that they form a solid line). The points are ordered so that points to the right are greater than points to the left:

Continued from Previous Slide: : 

Continued from Previous Slide: Every real number corresponds to a distance on the number line, starting at the center (zero). Negative numbers represent distances to the left of zero, and positive numbers are distances to the right. The arrows on the end indicate that it keeps going forever in both directions.

The End : 

The End By:-Parv Jain Flyers 2 G

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