Every real number sits in nested sets. Pick the tightest label that still fits: naturals ⊂ wholes ⊂ integers ⊂ rationals ⊂ reals; irrationals are reals that are not rational.

Steps

1. Natural numbers: 1, 2, 3, … (positive integers).
2. Whole numbers: 0, 1, 2, 3, …
3. Integers: …, −2, −1, 0, 1, 2, …
4. Rationals: fractions p/q with integers p, q ≠ 0 (includes terminating/repeating decimals).
5. Irrationals: reals that are not rational (e.g. √2, π when they appear non-perfect).
6. Reals: all of the above on the number line.