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 $$ \mathrm{sgn} (a) \cdot b.$$