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In my textbook there are sometimes points in the form $P(\pm a ; \pm b) \hspace{4cm}$(1).

This nevertheless is really ambiguous; as I understand, it could be either $P_1 (a;b)$ and $P_2(-a;-b)$ or all the possible combinations: maybe a clearer way to express those 4 points is $P_{1;2}(\pm a;b)$ and $P_{3;4} (\pm a ; -b)$

Is there a correct way to interpret the (1) or is it just ambiguous?

Edit: an example is $$\begin {cases} x^2+y^2=1\\ |y|=2|x| \end{cases} \Longrightarrow x^2=\dfrac{1}{5} \Longrightarrow x =\pm \dfrac{\sqrt5}{5}$$ We also have $y=\pm 2x$ so the points are $ \left(\pm \dfrac{\sqrt5}{5}; \dfrac{2\sqrt5}{5} \right)$ and $ \left(\pm \dfrac{\sqrt5}{5}; - \dfrac{2\sqrt5}{5} \right)$ My book has as solution $ \left(\pm \dfrac{\sqrt5}{5}; \pm \dfrac{2\sqrt5}{5} \right)$

Lorenzo
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    I think it would be helpful if you gave a more specific quote from your textbook. I think it is usual to interpret multiple instances of $\pm$ as being independent: so if you have $2$ instances of $\pm$, that's an abbreviation for $4$ cases. – Rob Arthan Dec 06 '24 at 22:35
  • Well I see this notation in the solutions of many problems, as example a system of equations – Lorenzo Dec 06 '24 at 22:39
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    So give us a specific example, then we may be able to give you some help without guesswork on our part. Help us to help you! – Rob Arthan Dec 06 '24 at 23:14
  • Edited, my question is general by the way: I am trying to know if there is a convention or if this is just bad notation – Lorenzo Dec 07 '24 at 07:35
  • $y=\pm x$ is shorthand for the disjunction "$y=-x$ OR $y=x$"; so, in the absence of context, $y=\pm x\pm z$ and $\pm y\ne \pm x,$ and even $y\ne\pm x,$ are all ambiguous. – ryang Dec 07 '24 at 14:11
  • Oh okay so logically when I say $x \neq \pm y$ it is only needed that at least one condition, either $x \neq y$ or $x \neq -y$ is satisfied. This, however, isn't correct since I need for both condition to be true at the same time. So this notation isn't just ambiguous, it is just wrong, am I right? – Lorenzo Dec 07 '24 at 15:01

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