- Numeral
\(\{0,1,2,3,4,5,6,7,8,9\}\)
- Counting Numbers
\(\mathbb{N}^+=\{1,2,3,4,\ldots\}\)
- Natural Numbers
\(\mathbb{N}=\{0,1,2,3,4,\ldots\}\)
- Integers
\(\mathbb{Z}=\{\ldots,-3,-2,-1,0,1,2,3,\ldots\}\)
- Negative Integers
\(\mathbb{Z}^-=\{-1,-2,-3,-4,\ldots\}\)
- Positive Integers
\(\mathbb{Z}^+=\{1,2,3,4,5,\ldots\}\)
- Rational Numbers
\(\mathbb{Q}=\left\{\samefrac ab\,\middle|\,a,b\in \mathbb{Z},b\ne0\right\}\)
- Irrational Numbers
Irrational numbers are the numbers, which are not rational numbers.
Cannot be written in the form of \(\samefrac ab\). \((\sqrt2,\sqrt3,\pi,e,\ldots)\) Irrational numbers are denoted with \(\mathbb{Q}'\).
- Real Numbers
\(\mathbb{R}=\mathbb{Q}\cup \mathbb{Q}'\)
\(\mathbb{R}=(-\infty,+\infty)\)
- Note
\(\mathbb{N}^+\subset \mathbb{N}\subset \mathbb{Z}\subset \mathbb{Q}\subset \mathbb{R}\)
- Prime Numbers
Positive numbers bigger than 1 which are only divisible by 1 and itself are called prime numbers.
\(2,3,5,7,11,13,17,\ldots\)
- Relatively Prime Numbers
Natural numbers which don't have a common divisor other than 1 are called relatively prime numbers.
(For example 8 and 15 are relatively prime numbers)