If, say, we know that $x=1$, is then the expression $x=\pm 1$ mathematically incorrect?
I ask this because when we use $\pm$ sign in the discriminant formula we imply that any of the plus or minus cases is possible. But in this case only one case is possible. Is it wrong to use $\pm$ sign here? How can I convey the difference in meaning?
[Math] About plus-minus sign
notation
Best Answer
If $x=1$, then $x=\pm 1$ is not incorrect, that is, it is not false.
The notation $x=\pm a$ is not an equality, it isn't saying that $x$ and $\pm a$ are the same thing, in fact $\pm a$ has no meaning by itself, it doesn't represent anything. An expression such as $x=\pm a$ should be read as a whole, as a unique symbol and it is simply short hand notation for $x=a \lor x=-a$.
In this particular case, since $x=1$ is true, then so is $x=1 \lor x=-1$, which is to say $x=\pm 1$ is true.