Cardinality of the continuum

The cardinality of the continuum refers to the size of the set of real numbers \(\mathbb{R}\). It is typically denoted by \( \mathfrak{c} \) (the letter "c" for "continuum"). The cardinality of the continuum is larger than that of the set of natural numbers \(\mathbb{N}\), which is countably infinite. To understand it in a formal context: 1. **Countable vs.