Exam-style question
Try this first
Explain how the natural, rational and irrational numbers relate to the set ℝ of real numbers.
Model answer
What a good answer should say
- The natural numbers are included in the real numbers.
- The rational numbers are also included in the real numbers and can be expressed as ratios of integers.
- Irrational numbers are real numbers that are not rational.
- Therefore, ℝ contains both rational and irrational numbers, including the natural numbers.
Explanation
Why this works
A complete answer identifies ℝ as the larger set, states that natural and rational numbers are included in it, and distinguishes irrational numbers from rational numbers while recognising that both are real.
Common mistake
No common mistake is linked to this question yet.