Besides being the first and last letters of the alphabet, why do we like abc and xyz so much?
In algebra, both abc and xyz are used, and occasionally pqr as well. Why those specifically? And for vectors, one of the notations is ij. Why is that? And in programming, it is a convention to use loops with ijk as the index. Why not something like cde (for count) or tuv(tally)? Why index? And in coordinates, we use xyz. Why is that? Why not abc? What about ijk, pqr, etc.? Also, why is y and z flipped in some 3D programs, and why is in some 2D programs, up is negative y rather than positive?
Finally, why do these kind of triplet letter combinations always use the Latin alphabet? Why aren’t there any conventions that use Cyrillic, Greek, Arabic, or the Latin letters with cool hats? Is it because English became the dominant language? That can’t be the only reason, as we still use some Greek symbols for some things like pi, phi, alpha(for angles as well as the particle), beta, gamma (rays), etc. The Greeks figured out things like coordinates, algebra, etc., so why Latin letters? Is it because of the Romans?
i,j,k for basis vectors is an interesting one. Historically, Hamilton invented his quaternions before any notion of “vector” existed (as an algebraic object; I believe the geometric notion is older). (So, what, did people just write out everything componentwise? Yes, yes they did. For example, that’s how things like Maxwell’s equations were originally presented.) The reason he chose i,j,k for the unit quaternions is because i was already in use for complex numbers, and i was in use for complex numbers probably to stand for “imaginary”.
The notion of “vector” was invented specifically as a “de-algebraicization” of quaternions. People did not like working with quaternions because they thought it was weird, particurlary because they required 4 numbers but space only required 3, so the likes of Gibbs and Heaviside gutted them and gave us modern 3D vector calculus. The reason we work with the dot product and cross product in 3D is specifically because, given pure imaginary quaternions v, w the product (vw) has real part (-v.w) and imaginary part (v x w).
Also, your last paragraph is somewhat misinformed. Sequences of Greek letters are used all the time, and Hebrew letters are also used in set theory to denote cardinalities (though I can only think of aleph and beth, no sequences of such letters). It is also well-known that some people like to use Japanese よ (yo) for the Yoneda embedding in category theory. But beyond Latin and Greek, there is quite a dearth.