Page 4 - 9 Math 2

2. Real and Complex Numbers eLearn.Punjab

For example, the numbers 2, 3, 5, p and e are all irrational numbers.
The union of the set of rational numbers and irrational numbers is
known as the set of real numbers. It is denoted by R,
i.e., R = QjQ/

Here Q and Q’ are both subset of R and QkQ/ =f

Note:

(i) NfWfZfQ
(ii) Q and Q/ are disjoint sets.
(iii) for each prime number p, p

is an irrational number.
(iv) square roots of all positive

non- square integers are
irrational.

2.1.2 Depiction of Real Numbers on Number Line

The real numbers are represented geometrically by points on a
number line l such that each real number ‘a’ corresponds to one and
only one point on number line l and to each point P on number line l
there corresponds precisely one real number. This type of association
or relationship is called a one-to-one correspondence. We establish
such correspondence as below.
We first choose an arbitrary point O (the origin) on a horizontal
line l and associate with it the real number 0. By convention, numbers
to the right of the origin are positive and numbers to the left of the
origin are negative. Assign the number 1 to the point A so that the line
segment OA represents one unit of length.

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