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: $\mathbb{N}\subset \mathbb{Z}\subset \mathbb{Q}\subset \mathbb{R} \subset \mathbb{C}$