Ker[cos(x)] Analysis: \pi \mathbb{Z} ± π/2

[Bachelier]

is it better to say $Ker[cos(x)] = \pi \mathbb{Z} \ {\color{red}-} \ {\Large{\frac{\pi}{2}}}\ \vee \ Ker[cos(x)] = \pi \mathbb{Z} \ {\color{red}+} \ \Large{\frac{\pi}{2}}$

 

[Fredrik]

Assuming that the former notation means
$$\left\{\pi n-\frac\pi 2\,\big|\,n\in\mathbb Z\right\},$$ and the latter means the same thing with + instead of -, then both notations represent the same set. I think I would just write
$$\left\{(2n+1)\!\frac\pi 2\,\big|\,n\in\mathbb Z\right\},$$ because "simple" notations like yours tend to require explanation. If you want a simple notation, then why not introduce a notation for the set of odd integers, say $\mathbb Z_\text{odd}$ and write
$$\mathbb Z_\text{odd}\frac\pi 2?$$
LaTeX tips: \operatorname{ker} and \cos x. $\operatorname{ker}[\cos x]$

 

[Bachelier]

Assuming that the former notation means
$$\left\{\pi n-\frac\pi 2\,\big|\,n\in\mathbb Z\right\},$$ and the latter means the same thing with + instead of -, then both notations represent the same set. I think I would just write
$$\left\{(2n+1)\!\frac\pi 2\,\big|\,n\in\mathbb Z\right\},$$ because "simple" notations like yours tend to require explanation. If you want a simple notation, then why not introduce a notation for the set of odd integers, say $\mathbb Z_\text{odd}$ and write
$$\mathbb Z_\text{odd}\frac\pi 2?$$
LaTeX tips: \operatorname{ker} and \cos x. $\operatorname{ker}[\cos x]$

Besutiful. Thanks.