Number sets ℕ, ℤ, ℚ, ℝ
Mark every number set the given number belongs to.
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Number sets fit inside each other: every natural number is an integer, every integer is rational and every rational number is real (ℕ ⊆ ℤ ⊆ ℚ ⊆ ℝ). Irrational numbers, such as √2 or π, cannot be written as a fraction. They belong only to the irrationals and to ℝ.
What does this generator do?
It shows a number and five buttons. On easy, the numbers are integers, fractions and decimals. On medium, square roots, recurring decimals and π appear. On hard, you first have to simplify the number, for example (√3)² or √2 · √8.
How to use it
1) Simplify the number if you can (√16 = 4). 2) Decide whether it can be written as a fraction. If yes, it is rational and belongs to ℚ and ℝ. If not, it is irrational. 3) If it is a whole number, it is also in ℤ, and if it is a positive whole number, it is also in ℕ.