How do I write n ∈ all of the known number sets

Question

If I want to say that n ∈ all of the known number sets do I have to write n ∈ $\mathbb{N} , \mathbb{Z} , \mathbb{Q} , \mathbb{R} , \mathbb{C}$ or should I just leave it blank?

Answer 1

If $n\in \mathbb{N}$, it is also in all the other sets you wrote.

Answer 2

If $n\in \Bbb{N}$, it follows that $n$ belongs to all of the other sets you listed since $\Bbb{N}$ is a subset of all of them.

$$\Bbb{N}\subseteq\Bbb{Z}\subseteq\Bbb{Q}\subseteq\Bbb{R}\subseteq\Bbb{C}$$

Answer 3

I believe $\mathbb{Z}_2$ is a number set as well, and smaller than $\mathbb{N}$.

And the set of imaginary numbers $\mathbb{I}$ has nothing in common with $\mathbb{N}$.

Answer 4

1) $n ∈ H$

2) $for all H ∈ \{\mathbb{N} , \mathbb{Z} , \mathbb{Q} , \mathbb{R} , \mathbb{C} \}$

observe that in step 2, I didn't use the inclusion, but H is indeed an element of this "weird" set of sets. example:

Using step 2, since H belongs to this set of sets, then it must be for example that $H=\mathbb{Q}$.

Then by step 1 $n ∈ \mathbb{Q}$