what is the symbol generally used for whole numbers?

Question

For subjecting to whole numbers, what symbol should I use? it must be valid for using anywhere from school to college. The symbol should be known and well proper to be understood easily by a school student.

Answer 1

You can use $\mathbb{Z}$ for the integers, i.e. the set of numbers $\{\cdots, -3, -2 ,-1, 0, 1, 2, 3, \cdots\}$.

Or you can use $\mathbb{N}$ for the cardinal numbers, also called the counting numbers $\{1, 2, 3, \cdots\}$. Sometimes $0$ is included in $\mathbb{N}$ as well.

Answer 2

$\mathbb N$ generally means $\{0,1,2,\dots\}$. It is called the set of natural numbers. (Note that sometimes $0$ is included, sometimes it isn't; it depends on the author. If you use the symbol $\mathbb N$, it's a good idea to specify what you mean.)

$\mathbb Z$ means $\{\dots,-2,-1,0,1,2,\dots\}$. It is called the set of integers.

If you want a way to refer to $\{1,2,3,\dots\}$ (i.e. without $0$) without ambiguity, you could write $\mathbb Z^+$. The superscript $+$ means you're talking about its positive elements.

Answer 3

When I was school in Scotland, it was W for whole numbers ie 0,1,2,... N for naturals it 1,2,3,...

Z for ...,-2,-1,0,1,2,3,...

At Oxford, N was 0,1,2,3,...

These days I use ${\Bbb N}$ for $0,1,2,....$ and ${\Bbb N}_1$ for $1,2,3,...$

The referees for my book "proof patterns" didn't like my notation and wanted me to change but I said no.