Zero And One

18 Dec, 2025

Number $0$ means none, nil. For any number $a$ ,

$\begin{matrix} 0 \times a & = 0 \\ 0 + a & = a \end{matrix}$ .

In the set of all multiples of 2 (such as $2, 8, 60 \dots$ ), there is no $1$ , but surprisingly there is $0$ .

This curious situation motivates comparing $0$ and $1$ .

Let us make a table here.

	contains 0	contains 1
multiples of n, $n \geq 2$	yes	no
multiples of 0	yes	no
multiples of 1	yes	yes

In summary, one has the capability to generate all positive integers while other positive integers does not. This is why other positive integers do not generate one, otherwise they will in turn, too, generate all positive integers via multiples. By contrast, $0$ is capable of being generated via multiple by all positive integers, even those non-one integers.