Real Numbers, denoted by R, include all numbers that can be represented on the number line.
Real numbers combine rational numbers and irrational numbers.
Real Numbers Include:
Key Features of Irrational Numbers
Real Numbers Classification Diagram
⭐ 5 Examples of Real Numbers (with Explanation)
📝Explanation: All rational & irrational numbers are real.
📝 Description: R = Q + P.
📝 Description: √(–4) = 2i → imaginary, not real.
📝 Description: Non-perfect square root → irrational → real.
📝 Description: All decimals (whether terminating, repeating, or non-repeating) belong to real numbers.
📝 Description: All real numbers lie on the real number line.
📝 Description: Real numbers are closed under addition.
📝 Description: Fraction of integers → rational → real.
📝 Description: N, W, Z ⊂ Q ⊂ R.
📝 Description: They include negative & positive & zero.
📝 Description: Non-terminating, non-repeating decimal → irrational.
📝 Description: Repeating decimal → rational → real.
📝 Description: Real numbers are dense → infinite between any two.
📝 Description: √49 = 7 → rational → also real.
📝 Description: √–9 = 3i → imaginary.
📝 Description: √3 and π are irrational → both real.
📝 Description: Rational + irrational always gives irrational.
📝 Description: √12 = 2√3
2√3 – √3 = 1√3 = √3
📝 Description: √7 is irrational but real.
📝 Description: Real numbers are closed under subtraction.
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