Problems of Traditional Math Notation (2004)

Re:Problems of Traditional Math Notation (2004) by yorwba on Sunday November 05, 2017 @11:28PM (#15633441)

Absolute value is ambiguous if you have more than one occurence, like |a|b|c| could be (|a|)b(|c|) or |a(|b|)c|. But as you said, gratuitous parentheses solve this problem. A good typesetting program will also let you display the outer bars larger than the inner ones, so you can match them up even without parentheses

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Re:Problems of Traditional Math Notation (2004) by thethirdone on Monday November 06, 2017 @12:00AM (#15633529)

> 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.

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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.

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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.

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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?

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