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Ker[cos(x)] Analysis

  1. Apr 21, 2013 #1
    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}} ##
    Last edited: Apr 21, 2013
  2. jcsd
  3. Apr 21, 2013 #2


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    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]##
  4. Apr 21, 2013 #3
    Besutiful. Thanks.
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