## Archive for the ‘“=”’ Category

### crossposted from a numberwarrior thread

*At least when I was at school we were correct in writing “Answer = “, even though the teachers hated it!*/— howardat58, upthread.

i’m more likely to’ve encouraged this behavior
than to’ve “hated” it.

but “Answer” is a pretty awkward variable-name
so, given a chance, i’m also likely to’ve made it
as plain as i could find a way to do that what i’d
*really* like to see is a clear

A = …. messy expression to be simplified

right at the beginning and *then* the

bit at the end. which gives a presentation
clearer than one is likely to find on the
blackboards unerased by the previous
class. alas.

because “define variables (with units) precisely”
is a *major* sticking point for *many* students
and i’m not just talking about Remedial Algebra.
one of my favorite-ever calculus tutees
refused my excellent advice on this subject
*many* times.

but without it, we simply *cannot* organize
our presentations coherently.

she finally… same calc ii student here…
couldn’t endure my continual insistence
on keeping equations balanced as she
wrote out her calculations. we broke up
over it.

the attitude seems to be “it’s all just
ritual-process calculation anyway
until i can get the Answer”, whereas
of course one seeks to instill instead
something like “the Answer is itself
a collection of equivalent statements
(leading to the value of a variable)”.

“scratch” work is *obviously* the enemy of clarity
and not just clarity of *presentation*.
having calculated out some expression,
let’s say correctly, one is in the position
of having to *do something* with the result.

but without the whole A = Answer format…
a “proof”, if you will… one is left with a
bunch of area-on-the-page with certain
code-strings (and scattered english)
bearing no particular *stated* relation
to one another at all.

and if Answer = “the thing i want to see”
i’m very likely to give ’em full credit.
but that won’t make it good work.

### and in the darkness bind them

this i vow. i believe in the power of symbolic-objects-carefully-defined. in the power of “math”, in other words. and the holiest-of-all-math-holies i swear i will keep most sacred.

oh, equal sign! great in perfection!
none are like thee in the power to reveal!
no not “continuity” nor “magnitude”…
nor even “quantity”… nay, *nothingness*!…
not even “infinity”…
how are we to speak
how are we to write
how are we to think…

& who’ll understand *any* parable
that won’t understand that there
even *are* any parables…

it depends what the meaning of “is” is.

otherwise, fuck it. what is *wrong*
or whatever.

and a very new year.

### there’s going to be a certain amount of fiddling around right in here. of course there’s a *better* way but what we’re after is the *easy* way. standards are great that’s why there’s so many *of* ’em.

$\equiv$$\leftrightarrow$$\Leftrightarrow$.

any luck? three different symbols, right?
an equal-sign-that-didn’t-know-when-to-stop;
a “left-and-right-arrow”; and a *double* leftrightarrow.
right?

okay. it appears to work on *this* set-up;
no telling what *your* mileage looks like
(just be sure that it *will* vary).

these symbols, then.

these symbols *all* stand for versions of
“two things have the same interpretation”.

there’s already a great deal of confusion
about (what i take to be) the *best-known*
symbol in this class: the *sign of equality*, “=”.
i’ve remarked on this phenomenon before.

but at the “math 366” level–my current class–
it becomes very important to be very careful to
*distinguish* between various notions of
“means the same thing as”.

but… how?

• ## (Partial) Contents Page

Vlorbik On Math Ed ('07—'09)
(a good place to start!)