I want to express the sign of $a$ multiplied by $b$ in a formula but do not know how to mathematically express the sign of $a$?
I am not sure but using the plus-minus sign isn't correct, is it?
In latex style I would write:
$\pm a \times b$
I want to express the sign of $a$ multiplied by $b$ in a formula but do not know how to mathematically express the sign of $a$?
I am not sure but using the plus-minus sign isn't correct, is it?
In latex style I would write:
$\pm a \times b$
Supposing $a,b\neq 0$, the sign of $ab$ is $\text{sgn}(ab)=\frac{\left|ab\right|}{ab}$ The sign of $a$ is $\text{sgn}(a)=\frac{\left|a\right|}{a}$ and so the [sign of $a$] times $b$ is nothing but $\frac{\left|a\right|}{a}b$
The correct way to formalize the sign of $a$ multiplied by $b$ is $ \mathrm{sgn} (a) \cdot b.$