📘 REAL NUMBERS – COMPLETE NOTES
📘 1. What are Real Numbers?
All numbers that can be represented on a number line are
called real numbers.
👉 Includes:
Natural numbers (1, 2, 3…)
Whole numbers (0, 1, 2…)
Integers (…–2, –1, 0, 1, 2…)
Rational numbers (fractions like 1/2, 3/4)
Irrational numbers (√2, π)
📘 2. Euclid’s Division Lemma
A very important concept!
👉 It states:
For any two integers a and b (b ≠ 0), there exist integers q
and r such that:
a = bq + r, \quad 0 \le r < b
Where:
a = dividend
b = divisor
q = quotient
r = remainder
