Question: I have this equation:

> 
> $$f(x)=\tan(x)$$
> 
> 
> 

I found the vertical asymptotes to be:

> 
> $$x=\frac{\pi}{2}k$$
> 
> 
> 

What is the proper notation for that k is equal to every odd number integer(negative,positive, and zero)?

$$k\in\mathbb{Z}$$ is for every integer, but is there such a symbol for every odd number integer? 

Natural numbers are positive, and sometimes zero counting numbers, my question is about integers not natural numbers.

Answer: 
they are $$(2k+1)\cdot \frac{\pi}{2}$$ with $$k \in \mathbb{Z}$$
Alternatively, you could write

$$x = \frac{\pi}{2}k \quad , \quad k = \pm1, \pm3, \pm5 \dots$$