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> Absolute value is ambiguous if you have more than one occurence, like |a|b|c| could be (|a|)b(|c|) or |a(|b|)c|. Yeah, I get the issue in general, but the qu
by thethirdone 9y ago
> Absolute value is ambiguous if you have more than one occurence, like |a|b|c| could be (|a|)b(|c|) or |a(|b|)c|.
Yeah, I get the issue in general, but the quote I referenced was specifically referring to the equations from Wikipedia.
My thought is that pretty much any mathematician would not choose to use absolute value bars in a case where it would be ambiguous. For example (|a|)b(|c|) would be instead written |ac|b and |a(|b|)c| would be written |abc|. And so unless it the equations are specifically about showing properties of absolute value (in which case just use parenthesis), I don't see a case where the ambiguity would pop up in real discourse.
- chongli 9y agoFor example (|a|)b(|c|) would be instead written |ac|b That changes the meaning. You're now relying on multiplication being commutative which is not true for all sets.
- netheril96 9y agoIt doesn't matter in practice. These two bars denote either absolute value, or norm, or determinant, all of which are real or complex numbers. People surely have the freedom to define a non-commutative multiplication with real/complex scalars, but have you ever seen one?
- thethirdone 9y ago> That changes the meaning. You're now relying on multiplication being commutative which is not true for all sets As I said at the end of my last comment: I don't see a case where the ambiguity would pop up in real discourse. If you are dealing with non-commutative objects you can deal with a few more parenthesis. Just like non-associative objects result in many more.