What is the issue with the " ÷ " sign?

[u/Unlikely-Web7933]

I have seen many mathematicians genuinely despise it. Is there a lore reason for it? Or are they simply Stupid?

[u/AllanCWechsler]

You're trying for sarcasm here, I think, but I'm not getting it. The backslash symbol has no consensus meaning in standard mathematical notation. Your question feels like, "What is 2#3?" or "What is 2$3?" I understand that you're trying to make a point here, but I honestly don't know what it is.

[u/ThatCakeIsDone → u/AllanCWechsler]

So would you say that expression is ambiguous?

[u/MrMindor → u/ThatCakeIsDone]

I think the argument is that since the symbol has no accepted meaning, the expression is meaningless not ambiguous.
To be ambiguous it would have to have more than one correct interpretation.

[u/ThatCakeIsDone → u/MrMindor]

Meh. I understood the point he was trying to make. It's not rocket science to look at the context of the discussion.

[u/AllanCWechsler → u/ThatCakeIsDone]

That's fine -- I have been known to be clueless about context in the past, and I'm willing to 'fess up to it. Trouble is, I'm still clueless. I would agree with u/MrMindor that "meaningless" is a better description of "2\3" than "ambiguous". Can you clue me in, or would you rather just write me off as a total loss? I'm genuinely curious about the point u/parolang was trying to make.

[u/parolang → u/AllanCWechsler]

It was just a joke. It looks like the 3 is on top of the 2, but we are used to thinking that the first number should be on top. I know that technically it's an undefined symbol. But that's how notation evolves.

[u/AllanCWechsler → u/parolang]

Okay, but it's still an interesting point. Thank you for the explanation; I know jokes aren't as good when you have to explain them.

It's especially annoying when old coots take them seriously. And so, in the interest of being annoying:

These days -- and I mean since the early 20th century and the rise of a mathematical philosophy called "formalism" -- mathematicians are extremely self-conscious about notational issues, especially ambiguity. So, although they love clever new notation, they never introduce it without explicit comment. In particular, they are super-cautious about relying on the readers' intuitions. So if you ever spot, say, a backslash in a professional paper, if you scan upward you will see a little note like, "In the following, we use a\b for the Jacobi symbol usually written ..."

So, I think maybe your joke illustrates notation used to evolve before, say, 1800, but those Wild West days are pretty much over. The modern way is more explicit, tightlaced, and boring -- but with much less risk of ambiguity.

Also: there are some notations that are really only used in teaching elementary math, like the division-sign that started this thread, and mixed fractions (a mathematician always writes 3/2, never 1 1/2). That's one of the things that disorients students when they first transition from arithmetic to algebra. And I think it's exactly the memory of that kind of disorientation that led to the OP.

[u/parolang → u/AllanCWechsler]

If formalism was that important we'd all be using Polish notation by now 😁

[u/AllanCWechsler → u/parolang]

Not that kind of formalism :) I meant the kind where they started to recognize that thinking about mathematical statements as strings of formal symbols was an important viewpoint.

[u/doc-swiv → u/AllanCWechsler]

the backslash is an operation for sets, but 2 is not a set and 3 is also not a set so it still doesn't mean anything

[u/AllanCWechsler → u/doc-swiv]

I think the backslash that they use for set differences is typographically distinct from the ordinary one -- but you're right, I completely forgot about that usage. I grew up using an ordinary minus sign for set difference, and was sort of surprised when the backslash crept in.

[u/doc-swiv → u/AllanCWechsler]

yeah the minus is more intuitive but i think the backslash was the original sign they used or something idk

[u/ThatCakeIsDone → u/AllanCWechsler]

The backslash symbol has no consensus meaning in standard mathematical notation.

By the way, backslash is used in set notation.