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notation
#2: Post edited
by
tommi
·
2023-03-22T07:53:19Z (over 1 year ago)
- Consider the claim
- $ |x| = \pm x $.
- I would interpret it as stating that $|x| = x$ and $|x| = -x$, thereby implying that $x = 0$.
- A user at Matheducators stackexchange interprets it as saying that $|x| = x$ or $|x| = -x$, which holds for all real numbers.
- I would typically use the notation to index solutions to an equation or some numbers I am going through; the roots of a second order polynomial being an elementary case, but not the only one. I might also use it as a shorthand if I need to calculate something for two things of opposite sign and figured I could both calculations at once.
Now I am wondering whether my use is typical of the mathematical community (yes, as far as I know) and whether the plus-minus sign has a rigorous meaning and, if so, how it relates to the equality with the absolute value.
- Consider the claim
- $ |x| = \pm x $.
- I would interpret it as stating that $|x| = x$ and $|x| = -x$, thereby implying that $x = 0$.
- A user at Matheducators stackexchange interprets it as saying that $|x| = x$ or $|x| = -x$, which holds for all real numbers.
- I would typically use the notation to index solutions to an equation or some numbers I am going through; the roots of a second order polynomial being an elementary case, but not the only one. I might also use it as a shorthand if I need to calculate something for two things of opposite sign and figured I could both calculations at once.
- It is pretty clear that my intuitions are in conflict here; in one case I consider $\pm$ to mean and, while in other, or. Is this just a mistake or is there something deeper going on here?
#1: Initial revision
by
tommi
·
2023-03-22T06:38:13Z (over 1 year ago)
The meaning of $\pm$
Consider the claim $ |x| = \pm x $. I would interpret it as stating that $|x| = x$ and $|x| = -x$, thereby implying that $x = 0$. A user at Matheducators stackexchange interprets it as saying that $|x| = x$ or $|x| = -x$, which holds for all real numbers. I would typically use the notation to index solutions to an equation or some numbers I am going through; the roots of a second order polynomial being an elementary case, but not the only one. I might also use it as a shorthand if I need to calculate something for two things of opposite sign and figured I could both calculations at once. Now I am wondering whether my use is typical of the mathematical community (yes, as far as I know) and whether the plus-minus sign has a rigorous meaning and, if so, how it relates to the equality with the absolute value.