## 2.1. Countable Infinity

### Definition 2.1.1: Cardinality

Let

**A**and**B**be two sets. We say that**A**and**B**have the same**cardinality**if there is a bijection*f*from**A**to**B**. We write*card(*.**A**) = card(**B**)
If there exists a function *f* from **A** to **B** that is
injective (i.e. one-to-one) we say that *card( A)
card(B)*

If there exists a function *f* from **A** to **B** that is
surjective (i.e. onto) we say that *card( A)
card(B)*