Numbers along with arithmetic operators.
Concept of counting or measuring. example 4 cows, 6 trees.
(a) Natural Numbers (N)
Numbers of the type 1, 2, 3, 4 ...
(b) Whole Numbers (W)
Numbers of the type 0, 1, 2, 3, 4 ...
(c) Integers (Z)
Numbers of the type ... - 3, - 2, - 1, 0, 1, 2, 3, 4 ...
(d) Rational Numbers (Q)
A number of the type p/q where p and q are integers and q ≠ 0.
(e) Irrational Numbers (I)
A (Real) number ‘i’ is called irrational if it cannot be written in the form p/q
where p and q are integers and q ≠ 0.
(f) Real Numbers (R)
Combination of real rational and irrational numbers
(g) Complex Numbers (C)
Numbers of the form a + bi where a, b are real numbers and i = squareroot - 1
CBSE Students Special for class X
A proven statement used to prove other statements
Given two positive integers a and b,( a >= b) there exists unique integers q and r satisfying a = bq + r, 0 < = r < b.
An algorithm is a series of well defined steps which gives a procedure for solving a type of
Euclid's Division algorithm
This is used to obtain the HCF of two positive integers, say a and b, with a > b, follow the steps below:
# Apply Euclid's division lemma, to a and b. So, we find whole numbers, q and r such that a = bq + r, 0 < = r < b.
# If r = 0, b is the HCF of a and b. If r not equal to 0, apply the division lemma to b and r.
# Continue the process till the remainder is zero. the divisor at this stage will be the required HCF.