# fundamental-sets2

Some sets are associated with these, conventinally used, identifiers:

* a set (generic set) is usually denoted by a single letter, $$S$$
  * or, if several are considered at the same time, $$A, B, C, \dots$$
* The empty set, $${}$$, has a special, unique symbol: $$\varnothing$$
  * there exists only one empty set.
* The universal set has its own letter, $$\mathcal{U}$$
  * it contains everything; there's only one universal set.
* The power set has its own letter, $$\mathcal{P}$$.
  * the power set of a set S is denoted by $$\mathcal{P}(S)$$.

The most fundamental number sets have their own unique identifier:

* ℕ, the set of the natural numbers, $$\mathbb{N}$$
* ℤ, the set of the integers, $$\mathbb{Z}$$ (from German *Zahl*)
* ℚ, the set of the rational numbers, $$\mathbb{Q}$$ (from *quotient*)
* ℝ, the set of the real numbers, $$\mathbb{R}$$
* ℂ, the set of the complex numbers, $$\mathbb{C}$$
* Their relation: $$\mathbb{N}\subset \mathbb{Z}\subset \mathbb{Q}\subset \mathbb{R} \subset \mathbb{C}$$