Numbers grew with human needs — counting led to fractions, debt led to negatives, geometry led to irrationals, and equations led to imaginaries.
Stages
- Naturals {1, 2, 3, …} — counting.
- Whole numbers {0, 1, 2, …} — add zero.
- Integers {…, −2, −1, 0, 1, 2, …} — add negatives.
- Rationals — fractions.
- Reals — add irrationals.
- Complex — add i.