Mathematical operation to simulate logical OR with boolean values $\textsf{false} = 0,\ \textsf{true} = \mathbb{R}^*$ The other day I was playing around with some equations I wanted to combine and came across this problem : Let's say I have two mathematical quantities $A,B \in \mathbb{R}$. Both can be either $= 0$ or $\neq 0$. Let's define the value $\textsf{true}$ to be "$\neq 0$" and $\textsf{false}$ to be "$=0$". So $A$ and $B$ now represent boolean value.
It is easy to mathematically simulate the AND operator by multiplying $A \cdot B$ since $A\cdot B\neq 0 = \textsf{true}$ iff $A \neq 0 = \textsf{true}$ and $B \neq 0 = \textsf{true}$
But how can we simulate the OR operator using only standard functions. (Typically not "case"-functions or piecewise-function) ?
I was thinking about using DeMorgan's Law and writing $A\vee B = \neg(\neg A \wedge \neg B)$, but now we need to mathematically write "$\neg$". The hard part here is that $\textsf{true}$ can be any number except $0$, not a fixed one.
I also tried to "normalize" the variable, for example by dividing it by itself but this then raises the problem of $0/0$ for $\textsf{false}$ variable. Ideally we would need an operation $F$ such that
$$
F(A) = \begin{cases}
C & \text{if } A \neq 0 \\
0 & \text{else}
\end{cases}
$$
(for some constant $C$).
Then $\neg A$ would simply be $C-F(A)$. 
Thanks :)
 A: Note that the problem disappears when you consider only non-negative real numbers instead of all real numbers: in that case you could just use '$+$' for OR.
So one way of reducing your situation to this one is by squaring the variables before adding them: $x \vee y := x^2 + y^2$.
(Perhaps you heard about the polynomial in 26 variables whose only output (if you feed it 26 integers) are prime numbers? It was produced by translating the concept of 'being a prime number' to relations between polynomials in pretty much the same way we are discussing here.)
EDITTED IN: a bit more about the prime polynomial can be found here: https://mathoverflow.net/q/132954/41139. Apparently I misremembered and the output (on integer inputs) may be either a negative number or a prime number but it is still pretty amazing that whenever the outcome is positive it is prime (and every prime appears in this way).
A: Extra answer:
Use $ X \vee Y = |X|+|Y| $  where $ |X| $ is the absolute value of X
Simulating logical NOT can be done like this:
$ \neg A = 1 -sign(|A|)$
hope that helps.
