An argument arising on Facebook. page 11

DarkBaron: I fail to see how that is an example of juxtaposition. That’s an integral of a Gaussian function — are you referring to b^2/4 + c? If so, the c is correctly not associated with the 4.

As an aside, however, pulling equations from Wikipedia doesn’t really count, since those equations are written with TexVC, which anyone can use when editing a wiki article. There are all sorts of convention rules that apply to creating well-formed expressions in Latex/Tex/etc, and so if you see an equation that is ill-formed, it is due to the fault of the user not being careful. There are “\frac” and “\over” commands, for instance, which are encapsulated division tools.

Matt: Agreed.

Of course. We know that from experience. But I bet I could find some people that say that the c is associated with the 4 due to what they’re used to, some of which are physics majors, so don’t necessary go assuming “oh they’re just dumb then and can’t apply simple algebra.”

Again, just because someone might think it’s “associated with the 4” doesn’t mean it’s ambiguous. It means the user is interpreting the formula incorrectly, especially when we know what kind of tools are being used to process those Wiki equations and what commands exist for creating formulations and encapsulations by convention.

Showing me an equation where there is no juxtaposition doesn’t prove your point. I’m asking for something where juxtaposition is present in a widespread way.

Clarification note: You shouldn’t be able to find any because it’s not a widespread system. Almost anything you find will either include encapsulating tools — and if it doesn’t, it won’t explain outright that it’s using a different system. So we’ll end up going back-and-forth on this all day assuming we reach that point. So, as Matt said, probably best to agree to disagree and be on our way.

TL;DR While [removed] might interpret it as “4+c” is the denominator, it doesn’t mean it’s ambiguous. They are objectively wrong (and not using another form of interpret the same equation – which would make it ambiguous) under the terms of PEMDAS, which is the most wide-spread system and should really be the only one taken in consideration.
The correct would be dividing b² by 4 and THEN adding c, btw.

Not to unnecessarily simplify the equation, but shouldn’t the Distributive Property apply before everything else?

6 ÷ 2(1+2) = ?
6 ÷ (2 + 4) = ?
6 ÷ (6) = ?
1 = ?

At least, that is how I learned how to interpret basic algebra equations.

Originally posted by dragoon1140:

Not to unnecessarily simplify the equation, but shouldn’t the Distributive Property apply before everything else?

6 ÷ 2(1+2) = ?
6 ÷ (2 + 4) = ?
6 ÷ (6) = ?
1 = ?

At least, that is how I learned how to interpret basic algebra equations.

Yes, distributive property says a(b+c) = ab + ac, but the question is what “a” is. Is a = 3 because of (6/2) or is a = 2 because of juxtaposition? That’s what we’re discussing ITT.

Nobody cares about this topic anymore. However, I was reviewing my old textbook in real analysis, and came across this gem (cf. Bartle and Sherbert, 4th Edition, pp. 175).

See! It does exist!