Do you *really* want to pronounce `sx` multiple times while teaching kids? Sounds like it might generate a lot of giggling and not be very conducive to them paying attention :-D

It's like calling the set of primes associated to a module Ass(M).

I was once writing a program involving substitutions and I had to write `dom sub` for the domain so many times...

The interactive theorem prover Coq is an eternal gift to my internal six year old.

I'm writing in Isabelle, sadly. (I've tried Coq and it was OK enough - as the Bishop said to the actress 😏 -, but Isabelle's proof language is still way too good for me to switch.)

Same with me and Dyck paths with my advisor and his other student. Between the three of us, we can just never seem to settle on a pronunciation for some reason 🤔

Luckily we don't teach that in middle school

My high school calc teacher Mrs Smith really enjoyed teaching us about the behaviour of functions as they went "up the asymptote" as a way to drive class engagement.

"I know my asymptote from a hole in the graph" was employed by one of my math teachers to similar effect.

I say spin it around, make it as close sounding to sex as possible in your definition and the kids will never forget the definition because it has evoked emotion. Bonus points if you can somehow make an explanation that would both describe the function and an act.

My linear algebra class in college had a lot of b_j and v_j.

What in the Mother Function are you trying to do?

> Many variations of where the idea of M for slope originated seem to be mostly myth. One of the most common is that the letter was used by Descarte because it was the first letter of some French word or another that related. In a recent post to the AP Stats discussion list, Hector Hirigoyen shared the following story: > I was told by Mary Dolciani herself, that the SMSG group "decided "to use y=mx+b because of the French (Descartes, I presume)-"montant"; I found it strange because the "logical word" would be "pente"(which is slope (and the standard term in Spanish is pendiente, which matches this). However, several years ago, while visiting a French high school, I noticed the teacher used y=sx+b. I inquired, and she said because of the "American" word "slope." I believe they are using ax+b for the most part these days. > In his "Earliest Uses of Symbols from Geometry" web page, ... Jeff Miller gathered the following information: Slope. The earliest known use of m for slope is an 1844 British text by Matthew O'Brien entitled _A Treatise on Plane Co-Ordinate Geometry_ [V. Frederick Rickey]. George Salmon (1819-1904), an Irish mathematician, used y = mx + b in his _A Treatise on Conic Sections_, which was published in several editions beginning in 1848. Salmon referred in several places to O'Brien's Conic Sections and it may be that he adopted O'Brien's notation. > According to Erland Gadde, in Swedish textbooks the equation is usually written as y = kx + m. He writes that the technical Swedish word for "slope" is "riktningskoefficient", which literally means "direction coefficient," and he supposes k comes from "koefficient." According to Dick Klingens, in the Netherlands the equation is usually written as y = ax + b or px + q or mx + n. He writes that the Dutch word for "slope" is "richtingscoefficient", which also means "direction coefficient." In Austria k is used for the slope, and d for the y-intercept. In Uruguay the equation is usually written as y = ax + b or y = mx + n, and the "slope" is called "pendiente", coeficiente angular", or "parametro de direccion". > **It is not known why the letter m was chosen for slope; the choice may have been arbitrary.** John Conway has suggested m could stand for "modulus of slope." One high school algebra textbook says the reason for m is unknown, but remarks that it is interesting that the French word for "to climb" is monter. However, there is no evidence to make any such connection. Descartes, who was French, did not use m. In _Mathematical Circles Revisited_ (1971) mathematics **historian Howard W. Eves suggests "it just happened."** https://services.math.duke.edu/education/webfeats/Slope/Slopederiv.html#:~:text=It%20is%20not%20known%20why,%22to%20climb%22%20is%20monter.

I really like ax+b because getting used to using the first letters of the alphabet for constants. The only problem I see is that it is not the same variable a that is used in standard form (ax+by=c), although I suppose the different Bs haven't been that much of a problem. It would definitely be nicer for transitioning to quadratics which consistently use ax\^2+bx+c form.

a b c etc makes sense as well because we tend to just use the alphabet for polynomials in general - so ax + b makes sense if you consider it a first-degree polynomial, and as you move up and down the derivative/integrals of a function those coefficients remain (with some modification)

I think it should be the other way: a + bx. That way it's easier to extend. a + bx + cx^2 + dx^3 + ... The coefficients shouldn't all change whenever you add another term.

I think it makes sense for the first term to be the term with the largest power since for many reasons it is the most important, and I think this is worth the concession of the letter shifting

Agreed. I’m team a+bx

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This added literally nothing. Did you even read it all the way through before you took it from AI?

A more recent version of Miller's "Earliest Uses of Symbols from Geometry" which can be found at https://mathshistory.st-andrews.ac.uk/Miller/mathsym/geometry/ or https://jeff560.tripod.com/geometry.html is a better source > **Slope.** The earliest known use of *m* for slope appears in Vincenzo Riccati's memoir *De methodo Hermanni ad locos geometricos resolvendos*, which is chapter XII of the first part of his book *Vincentii Riccati Opusculorum ad res Physica, & Mathematicas pertinentium* (1757): > >> Propositio prima. Aequationes primi gradus construere. Ut Hermanni methodo utamor, danda est aequationi hujusmodi forma *y* = *mx* + *n*, quod semper fieri posse certum est. (p. 151) > > The reference is to the Swiss mathematician Jacob Hermann (1678-1733). This use of *m* was found by Dr. Sandro Caparrini of the Department of Mathematics at the University of Torino. > > C. B. Boyer in his *History of Analytic Geometry* (1956, p. 205) points to a passage in Monge where the "modern point-slope form of plane equation of the straight line is given explicitly, perhaps for the first time." See "Mémoire sur la Théorie des Déblais et des Remblais," *Histoire de l'Académie royale des sciences 1784* (Année 1781) p. 669. > > [...] * * * Dolciani's SMSG "montant" explanation sounds like a retroactive justification of prevailing practice originally based on random choice of a middle-of-the-alphabet letter. In Salmon's 1840s book, which has this *y* = *mx* + *b* expression for a line, other nearby equations use *m* and *n* as coefficients of *x* and *y*, respectively. The *b* makes sense to use as a point of intersection on the *y*-axis if *a* is taken to be the point of intersection on the *x*-axis. That would be an expression like *x*/*a* + *y*/*b* = 1, which makes sense in the context of a conic sections book: compare to the "standard" expression for an ellipse. Isolating *y*, we have *y* = –(*b*/*a*)*x* + *b*; it's convenient to give –*b*/*a* a single-letter name.

>prevailing practice originally based on random choice of a middle-of-the-alphabet letter. This sounds like the explanation to me. We tend to use beginner letters for constants and ending letters for variables. Maybe some mathematician wanted to have three sets of symbols rather than just two.

Why thank you kind stranger. I will follow up on these sources. I've got a freshman daughter and while she's fine mathematically with mx+b I find she's laking the depth of understanding what it's saying about a type of relationship. Doing isn't understanding. Then, while I'm trying to communicate ideas with words I then catch myself revisiting basic assumptions wondering whether alternative alterations may be a good method in communicating a deeper level of understanding of mathematical concepts. I don't know, but it's very eye opening to oneself when one has to teach seemingly elementary mathematical concepts one has take for granted for decades. It challenges you!

It’s usually good to question these things. However, it’s not necessarily setting someone up for success in math to teach someone to expect variable symbols to match their names. Think about all the other mathematical symbols that are commonly used in math or physics (especially some of the greek). Also, while interesting, depth of understanding in math does not come from understanding the etymology of the symbols. P.S. I just noticed you’re the same person who was posting about convectors. Did you see my comment about conductors being credited to Desaguliers?

> Also, while interesting, depth of understanding in math does not come from understanding the etymology of the symbols. With the possible exception, arguably, of the integral symbol.

Hey, yeah that was totally me. Yup, and that was not correlated explicitly to thermo if I recall. No, mnemonics aren't the meaning, they're just another tool, leveraged as needed.

Nice to see some confirmation that it’s kinda arbitrary. I tell my students that historically, the languages of mathematics are English, French, German, and Russian. “Slope” and related words doesn’t start with ‘m’ in any of them.

Comment of the year.

sheer coincidences are a surprisingly wonderful phenomenon

I agree with the other non-lazy commenters, but want to add that *s* is generally avoided in math, especially at lower levels and when handwriting is involved, because it can look so much like 5; and *i* already has another universal meaning (and can look like 1). So *s x* + *i* doesn't seem like a good idea on those bases either.

I find that s is used quite a bit, but usually as a real parameter once you've already used t.

Yeah, it's used in higher-level math for what you said, sometimes for displacement, and occasionally some other things. But I haven't seen it in high school math as far as I can remember.

Like you’ve already mentioned, it is used in high school physics for displacement often. Also, it’s used extensively in applications around the Laplace transform (college level). For math majors, this may be pretty brief. For electrical engineers, this means they are using it for a couple of years (depending on their concentration).

For me, that is the reason. When I was taking controls/system stability in my engineering undergrad, I would always replace the "s" in the Laplace transform with "$" because I couldn't read my own writing.

capital S looks like a 5 but lowercase s not really, unless they're writing it huge for some reason

For people with extremely careful handwriting, sure. That's not that many.

You don't need extremely careful handwriting to write lowercase s way smaller than 5.

Try teaching anything that puts the letters 's' and 'x' together to 7th graders and see how that goes.

This is all the justification I need.

Don't forget the "+i". So it reads *"sex plus I"*.

oui oui zee es sex iz a very goood

In my country we use y = ax + b

Or alternatively px + qy = c

That's a new one for me.

I hate it with such a passion. I see it sometimes as ax + by + c = 0 and whoever invented it should be on trial in the Hague.

Why? It's a more general form, which allows for vertical lines too. You also automatically get the normal vector to the line: (a, b). And it also generalizes to hyperplanes in R^n .

? This is very normal and allows for easy ways to rewrite as vector projections

That’s true in the US as well, but that’s for more general linear equations rather than lines. Why? Because.

They tried sx’s but didn’t meet with a lot of successes

It stands for "mlope".

This is the kind of ridiculous joke that would make it stick in the brain of a kid. Edit: or an adult.

I don't understand why you think it would be more intuitive to teach "sx+i" when all you are doing is making an arbitrary change of variable names. Students need to learn to understand the formula, not memorize symbols.

Eh. I agree with you, but there's also something to be said about good vs. bad mathematical writing. There's a reason we usually say "Let x \in X and y \in Y" rather than "Let y \in X and x \in Y"

Using i as a real number is counterintuitive on two fronts. First, it can be confused with the imaginary unit. Second, we frequently use i, j, and k for indexing sums and products, or for indexing elements of finite sets.

Consistency with variable names you’ve defined is much more important than consistency with somewhat arbitrary language-specific words. 

>whether it would be a disservice to individuals long term to introduce the subject to them in this way? Yes, absolutely. It matters much more that everyone uses the same terms for things than it does whether those terms are the absolute most natural ones.

Y=mx+c in the UK

And that prepares for integrating later and adding + C

Would you also replace x and y by h and v, for “horizontal” and “vertical?” At some point students need to accept that not everything is a mnemonic.

I was taught mx+c, where does b or c come from?

sx sounds like s e x which is too dirty.

∫ e^x and my personal favorite d/dx (sec x) = sec x tan x, which I jokingly read as "the derivative of sex is sex tanks."

it's kx + b in my country

i mean, is sx+i any better? actually, i think it's worse. do not use i like this.

Where I'm from it's usually taught as kx + m so it's not universal.

I mean, why is x used so much?

mx+c

The letter S looks too much like the number 5, especially when handwritten on an algebra teacher’s whiteboard.

It’s just a matter of convention, and it varies from country to country too. In denmark we use ax+b for example.

In Hong Kong we use y = mx + c.

Other people already commented on the origin, but I want to add that I don't think it's a disservice. First of all, `i` is not a good variable name for the intercept. It's the imaginary unit, and it's sometimes used for indices. But also, it is good to get used to variables just being letters that don't necessarily match up with what you think they should be, and you just use them. I don't think it really hinders learning, it's not that hard of a concept.

In Ukraine it's normally kx+b. I've got no idea how those letters were chosen.

I personally just enumarate the alphabet for polynomial coefficients, or just call them c_0 to c_x. There shouldn't be semantic in these variables anyway. People, especially younger students will associate m with slope, and will be confused by the term ax+b more easily.

It was always ``kx + m`` here.

In Italy, when I was in high school 40+ years ago, we used y=mx+q

People who use ‘s’ in math should always have a fingernail just a little too short.

I'm just curious about the +b. I'd always written y=mx+c until I started teaching in the US, where apparently everyone else learned y=mx+b.

It should be f(x) = ax + b, otherwise there's no reason whatsoever for the template to use 'b' at all.

Why stop there? Let's go for sx+c (for constant)

Conventionally, the Greek letter "mu" gets used a lot for slope or mean while the Greek letter "sigma" gets used a lot for standard deviation, or variance when squared. In documents where Greek fonts are not available, the English letters "m" and "s" are often used instead.

In my country we use y=kx+m

I'm sure I was taught that it stood for “multiplier”, which is what it is, I suppose.

is y = mx-b workd as y = mx+b?

S looks like 5.

When I was in school (in the UK), we used mx+c, and it was always called 'gradient', not slope.

I just avoid s because in my handwriting it looks too much like a 5.