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Q&A The meaning of $\pm$

2 answers  ·  posted 1y ago by tommi‭  ·  last activity 1y ago by Derek Elkins‭

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#2: Post edited by user avatar tommi‭ · 2023-03-22T07:53:19Z (about 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 user avatar tommi‭ · 2023-03-22T06:38:13Z (about 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.