### Let A~B Denote “A is Confused With B”…

Part of my job (as I see it from here) is to break students of nasty habits like writing “+” when they mean “and”.

Because, look. Suppose you know that A = B. Suppose you also know that C=D. You’d have to be pretty doggone obtuse to believe that you now know anything resembling A=B+C=D, right? I mean, come on now. How did “A” get to be equal to “B+C” all of a sudden out of thin air?

So if we want to abbreviate… and we sure as blue blazes do (the statistics books are wrong, wrong, wrong)… the (conjunctive meaning of) the English word “and” in contexts like this, it’ll be a good idea to introduce another symbol.

If typesetting were easy, it’d now be the “logical and” symbol (TeX “wedge”) $\wedge$ (thus: $A=B \wedge C=D$). But typesetting is not easy and we’re opting for plain old ampersand: “&” (thus: A=B & C=D).

Sounds simple, no? It’s never simple. I’ve just made “&” into a technical term and it’ll be subject to the same kind of abuse I’ve just illustrated. This is probably a bad idea just now… that’s why it’ll sometimes be worth the trouble to use “$\wedge$“.

But then… and I’ve now experienced this firsthand, maybe for the first time… even a special symbol like $\wedge$ will have an irresistible appeal for some students: “Which elements of {5, 4, 11, 6} are even?— 4$\wedge$6 — Oh dear me no… number-wedge-number?… what would that even mean (we wedge propositions or logical variables or things like that, don’t we)… admittedly this improves on “plus” but… but… can’t you just see how ugly this is?!”

It’s my belief that this kind of mishmoshing of Text and Symbols is actually encouraged by almost all math textbooks. I’m not now proposing another rant about a textbook (that will probably come later).
There’s a lot of great stuff in Epp; heck, there’s a lot of great stuff in the two chapters we’ve considered (very briefly in the case of Ch. 3). I myself have learned a new usage (Epp’s use of $\Rightarrow$ as opposed to $\rightarrow$… I’m Vlorbik and I approve of making the appropriate [particular-versus-global] distinction with these notations…) and mini-lesson-plans (every good problem suggests a line of attack…).