Real number Examples
Real number Examples
Real Numbers are a set of al numbers `x' such that `x' relates to a point on the number line.
The group of real numbers comprises of entire set of the rational numbers as well as the
irrational numbers. To understand the real numbers examples, consider given set S = 3 / 61,
28, - 3, - 31, 0, 1.7, - 612, 8, - 5 / 4, 16, - 5 1/2, . Now, make a list of al the constituents of
the set S that belong to the set of:
a) Integers,
b) Whole numbers,
c) Natural numbers,
d) Irrational numbers,
e) Irrational numbers, and,
f) Real numbers
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Let us first rewrite the elements of the set S in simplified manner.
S = 3 / 61, 256, - 3, - 31, 0, 1.7, - 612, 8, - 5 / 4, 4, - 11 / 2,
We can clearly classify the elements of the set in the fol owing way:
28, 16, - 5 1/2,
a) Integers: 256, - 31, 0, - 612, 8, 4
b) Whole numbers: 256, 8, + 4
c) Natural numbers: 0, 256, 8, + 4
d) Irrational numbers: - 3,
e) Rational numbers: 256, - 31, 0, - 612, 8, 4, 3 / 61, - 5 / 4, - 11 / 2, 1.7
f) Real numbers: 3 / 61, 256, - 3, - 31, 0, 1.7, - 612, 8, - 5 / 4, 4, - 11 / 2,
Thus, al the elements of the set S are indeed real numbers examples. Just about whichever
number you can think of is an example of a Real Number. The only numbers that are not real
are included in the set of complex numbers (or the imaginary numbers). The Real Numbers
were not given an identifying name prior to the discovery of the Imaginary Numbers. They
were cal ed `Real' since they were not imaginary.
All numbers on the number line are the real numbers. This list consists of (but is not restricted
to) positive and negative numbers, integer figures and all the rational and irrational numbers
(like square and cube roots, etc.). The set of real numbers is indicated by `R'.
Some properties of the Real Numbers are described below:
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Consider three numbers X, Y and Z, which belong to the set of real numbers.
1. Commutative Property for Addition and Commutative Property for Multiplication of real
numbers holds true.
a. X + Y = Y + X
b. X * Y = Y * X
2. Associative Property for Addition and Associative Property for Multiplication also holds true.
a. X + (Y + Z) = (X + Y) + Z
b. X * (Y * Z) = (X * Y) * Z
3. Identity Property for Addition and Identity Property for Multiplication are verifiable.
a. X + 0 = 0 + X = X
b. X * 1 = 1 * X = X
4. Inverse Property for Addition and Inverse Property for Multiplication are also verifiable.
a. X + (- X) = - X + X = 0
b. X * 1/X = 1/X * X = 1


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