Which of these is the correct way of saying "given that"?

Question

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.

Answer 1

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.