Re:Problems of Traditional Math Notation (2004)
by chongli on Monday November 06, 2017 @08:51AM
(#15635362)
For 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.
Re:Problems of Traditional Math Notation (2004)
by thethirdone on Monday November 06, 2017 @12:04PM
(#15636849)
> 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.
Re:Problems of Traditional Math Notation (2004)
by netheril96 on Monday November 06, 2017 @10:52AM
(#15636286)
It 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?
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.