Number - Number systems notation

Numbers are classified into specific sets: Natural Numbers ($\mathbb{N} = \{0, 1, 2, 3, ...\}$), Integers ($\mathbb{Z} = \{..., -2, -1, 0, 1, 2, ...\}$), Rational Numbers ($\mathbb{Q}$), Irrational Numbers ($\mathbb{Q}'$), and Real Numbers ($\mathbb{R}$).

A Rational Number ($\mathbb{Q}$) is any number that can be expressed in the form $\frac{p}{q}$ where $p, q \in \mathbb{Z}$ and $q \neq 0$. These include terminating decimals (e.g., $0.25$) and recurring decimals (e.g., $0.333...$).

An Irrational Number ($\mathbb{Q}'$) cannot be written as a simple fraction. Their decimal expansions are non-terminating and non-recurring (e.g., $\pi$, $\sqrt{2}$, $\sqrt{5}$).

Set notation symbols include: $\in$ (is an element of), $\notin$ (is not an element of), and $\subset$ (is a subset of). The hierarchy is $\mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \subset \mathbb{R}$.

Scientific Notation (Standard Form) is used to write very large or very small numbers in the format $a \times 10^k$, where $1 \le |a| < 10$ and $k$ is an integer.