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For example, I want to say

"Given that $\alpha$ is not infinity, $\alpha$ is not infinity. (Stupid example but just an example)"

Which of these is the correct way of saying it?

  1. $\alpha \ne \infty | \alpha \ne \infty$
  2. $\alpha \ne \infty : \alpha \ne \infty$
  3. $(\alpha \ni (\alpha \ne \infty)) \ne \infty$
  4. Given that $\alpha \ne \infty$, $\alpha \ne \infty$. (Don't say it in mathematical notation, but rather in words)
  5. Something else?

My first approach was to use the pipe sign "|", but I noticed that it can also mean division or "shortest distance from a line/point to another line/point". So maybe it's bad practice because "ambiguity sucks"?

I am therefore confused on what symbol (if any) to use when mathematically expressing the idea "given that".

Also, if more than one of these are accurate, then in what situations should I use what?

Thank you very much for the help.

Peashooter8890
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  • You could say it in the following way: $;\color{blue}{\alpha\ne\infty\implies\alpha\ne\infty},.$ – Angelo Feb 05 '23 at 07:47

1 Answers1

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I think that the only notation that would make sense is the following (the example is mine):

$ \alpha < 0 \implies \alpha \neq 1 $

(read "if $\alpha < 0$, then $\alpha \neq 1 $", or, in your preferred choice of words, "$\alpha \neq 1 $ given $\alpha < 0$")

However, I suggest you don't use symbols and use words instead.

Alex
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  • Would this be true for cases that aren't the reflexive property, like

    $a \ne 3 $ given that $a > 4$?

    (Question answered, thank you)

     – Peashooter8890 Feb 05 '23 at 04:01
  • I edited my answer by introducing a nonreflexive example. This should clear things up. – Alex Feb 05 '23 at 04:05
  • I have one last question.

    For something like "An equation in the form $ax^2$ given that $a \ne 0$ will have a derivative greater than 0."

    , should I leave it as is and try not to use further signs? If I do use signs, how would I do it?

     – Peashooter8890 Feb 05 '23 at 04:10
  • You're asking a question that should be asked separately. – Alex Feb 05 '23 at 04:29
  • Ok I am creating a new question right now – Peashooter8890 Feb 05 '23 at 04:47