Revision Notes on Real Numbers
Euclid’s Division Lemma
It is basically the restatement of the usual division system. The formal statement for this is-
For each pair of given positive integers a and b, there exist unique whole numbers q and r which
satisfies the relation
a = bq + r, 0 ≤ r < b, where q and r can also be Zero.
where ‘a’ is a dividend, ‘b' is divisor, ‘q’ is quotient and ‘r’ is remainder.
∴ Dividend = (Divisor x Quotient) + Remainder
Natural Numbers
Non-negative counting numbers excluding zero are known as natural numbers.
i.e. 5, 6, 7, 8, ……….
Whole numbers
All non-negative counting numbers including zero are known as whole numbers.
i.e. 0, 1, 2, 3, 4, 5, …………….
Integers
All negative and non-negative numbers including zero altogether known as integers.
i.e. ………. – 3, – 2, – 1, 0, 1, 2, 3, 4, …………..
Algorithm
An algorithm gives us some definite steps to solve a particular type of problem in a well-defined
manner.
Euclid’s Division Lemma
It is basically the restatement of the usual division system. The formal statement for this is-
For each pair of given positive integers a and b, there exist unique whole numbers q and r which
satisfies the relation
a = bq + r, 0 ≤ r < b, where q and r can also be Zero.
where ‘a’ is a dividend, ‘b' is divisor, ‘q’ is quotient and ‘r’ is remainder.
∴ Dividend = (Divisor x Quotient) + Remainder
Natural Numbers
Non-negative counting numbers excluding zero are known as natural numbers.
i.e. 5, 6, 7, 8, ……….
Whole numbers
All non-negative counting numbers including zero are known as whole numbers.
i.e. 0, 1, 2, 3, 4, 5, …………….
Integers
All negative and non-negative numbers including zero altogether known as integers.
i.e. ………. – 3, – 2, – 1, 0, 1, 2, 3, 4, …………..
Algorithm
An algorithm gives us some definite steps to solve a particular type of problem in a well-defined
manner.
