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I have an expression that contains arbitrary complex parameters $\mu_1$ and $\mu_2$. Additionally this expression contains a parameter $\sigma$ that is boolean like (takes values 1 or 0). The expression is:

$$v=\sigma v_1+\mu_1 v_2+\mu_2 v_3$$

Is there some mathematical convention how to treat boolean variables? Is there a special term for them (like binary/boolean variable)? And are there any preferred symbols that are used for such variables?

Thank you alot for reading my question.

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Your expression is valid if all the variables involved are in some ring such as the reals, otherwise it is invalid unless you have defined addition and multiplication of the involved objects (which you could). But if $σ$ is boolean then one common notation is "$\mathbf{1}_σ$" to denote the indicator variable which is $1$ if $σ$ is true and $0$ otherwise.

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  • $\begingroup$ I am not really using boolean variables. It is just a variable that takes the values 1 or 0. $\endgroup$ – MrYouMath Aug 15 '16 at 10:32
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    $\begingroup$ @MrYouMath: Then my first sentence applies. There's no particular convention for such variables. After all, there are only so many letters in the alphabet and that is it. And you can call your $σ$ an indicator variable. $\endgroup$ – user21820 Aug 15 '16 at 10:42

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