The same symbol means different things in different branches of math

[kane_magus]

(EDIT 2)

Nah, this isn't really a serious entry, but a half-assed, failed attempt at humor. The point remains that math (and code) can have way too many reused symbols with different meanings at times, but feel free to ignore all that pseudo-ranting at your leisure.

*insert the open "tongue-in-cheek mode" tag here*

(/EDIT 2)

Why can't math just keep its symbols and meanings separate and distinct? Huh? Why?! Is that too much to ask?!

Take this one for instance: (+) Just pretend that this is a circle with a plus sign inside of it. Ok, in one of my math classes, MAT250 (Linear Algebra), that symbol can mean either external direct sum or internal direct sum, depending upon the context, and they're two different things. We've been doing a lot with the two of those in the past few days, and it was mostly what the homework that's due tomorrow was about.

So, of course, it totally confused me for a couple of seconds just now when I was looking over the midterm of the previous semester's MAT258 (Discrete Mathematics) class in preparation for our midterm tomorrow. The first problem asked for the construction of a truth table of ¬(p (+) q). I was sitting there for a second or two all like "What? Why is it asking for the negation of the direct sum? Does it mean internal or external? How the hell do you even make a truth table for that anyway?" And then my brain finally switched over to MAT258 instead of MAT250, and I realized it was asking for exclusive or, which is what the (+) symbol means in propositional logic and which is something we haven't messed with for a few weeks now in that class.

Kane_Magus bashes the wall with his head. Repeatedly.

(EDIT)

Holy shit. And later on in that MAT258 sample midterm, the same goddamn symbol was used again, but this time it meant symmetric difference instead of exclusive or. Wow. *head asplode again*

...oh, wait. Those mean the same thing. Duh. So this time, it was just a terminology difference instead of a difference in meaning. Which is just as fucking bad. There is just as little reason to have three or four different phrases or terms for the same thing as there is to use the same symbol to mean three or four different things. Gah.

(/EDIT)

(EDIT 2)

*insert the close "tongue-in-cheek mode" tag here*

(/EDIT 2)

Comments

[jaytan.livejournal.com]

I am aware this is probably not the kind of response you want at all, but here I go anyway:

You should consider looking at the mathematical definition of an operator - its really not the foreign if you have dealt with operator overloading in C++:

A binary operation * on a set S is a function mapping S x S into S. For each (a, b) in S x S, denote *((a, b)) of S by a * b.

which you could translate to C code as a templated function:
template <typename S>
S operator*(S lhs, S rhs)
{
// do something
}

Once you get a grasp on this concept seeing the same symbol in different places will be less confusing. Its no different than seeing "1 << 5;" and "cout << 5;" in the same block of code.

[kane-magus.livejournal.com]

(Not sure what's up with commenting, because I thought I already posted this once, but it's not showing up for some reason.)

Eh, my post was more intended to be a tongue-in-cheek, supposedly humorous, pseudo-bashing of math in general (and, now that you bring it up, coding too) than a serious "I don't get this!! Please help!!" kind of post. The humor, such as it was, obviously didn't translate well at all here, what with this being plain text on the Internet and all.

[jaytan.livejournal.com]

Yeah I realized you weren't asking for help but I didn't really pick up on the humor. I was wasting time browsing the digipen friends page while waiting on someone and that reply helped me waste more time!