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State/Counting multiples of d between 1 and n
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Proposition: (Counting multiples of d between 1 and n) Suppose that $d \in \NN$ and $d \neq 0$. Suppose that $n \in \NN$ and $n \neq 0$. Let $S = \{1, \ldots, n \}$. Define $$S_d = \{ x \in S \mbox{ such that } x \mbox{ is a multiple of } d \}.$$ Then $$\vert S_d \vert = \lfloor \frac{n}{d} \rfloor.$$
Logical Connections
This statement logically relies on the following definitions and statements: Def/Floor
The following statements and definitions rely on the material of this page: State/Canonical decompositions of factorials, and State/Computing the totient of a prime power
To visualize the logical connections between this statements and other items of mathematical knowledge, you can visit the following cluster(s), and click the "Visualize" tab: Clust/Basic number theory, Clust/Basic counting
