Multiple set

In mathematics, the multiple set is the set of all multiples of a natural number . It consists of all natural numbers that are divisible by the original number without a remainder .

So: for a ${\displaystyle \mathbf {V} _{a}={\Big \{}d\in \mathbb {N} _{0}{\Big |}\ a|d{\Big \}}}$ ${\displaystyle a\in \mathbb {N} _{0}}$

The multiple of 7, for example, consists of all natural numbers that are divisible by 7 without a remainder, i.e. of the following elements :

${\displaystyle \mathbf {V} _{7}=\{0,7,14,21,28,35,42,49,56,63,70,77,84,...\}}$

For the sake of clarity, a multiple set is noted in an ordered manner.

Mightiness

The number of multiples of a natural number is countably infinite .

See also

• Divisibility
• Least common multiple
• Partial set

Web links

• Video: The multiple set . Pedagogical University of Heidelberg (PHHD) 2012, made available by the Technical Information Library (TIB), doi : 10.5446 / 19845 .