Do all mathematical symbols in LaTeX have a meaning?

Question

I debated whether I should post this on the TeX forum or here. Mathematics seemed more appropriate.

LaTeX has a ridiculous amount of symbols, including countless variations of the integral sign and variations of the logical symbols. So while looking through the compendium of symbols I began to wonder, "I've never seen half (probably more than half) these symbols ever used, what do they even mean?" So I began to wonder if they (the symbols that I have never seen) even had a formal or informal meaning.

So, in summary, do all of the symbols in LaTeX have a meaning, or are their meanings to be defined by the user, who is in need of new notation?

Just going to upload screen cap of symbols,

Answer 1

I guess you can make all the symbols have mathematical meanings, you can just take a symbol you like and assign to it a special meaning. For example let $\daleth_k(n)$ be the number of bijections from a set of size $n$ to the same set of size $n$ which contains no cycles of length less than $k$.

Answer 2

No. Counterexample:

$\aleph$ has a meaning (initial ordinals), $\beth$ has a meaning (power set cardinals), even $\gimel$ has a meaning (a cardinal function $\gimel(\kappa)=\kappa^{\operatorname{cf}(\kappa)}$).

But $\daleth$ doesn't have a meaning.

(The first four letters of the Hebrew alphabet are $\aleph,\beth,\gimel,\daleth$.)

Answer 3

$\LaTeX$ is not only for mathematics. For symbols you have: zodiac signs, cards suits, emoticons, etc... To see the capabilities of $\TeX$ and $\LaTeX$ check this awesome answers: https://tex.stackexchange.com/questions/1319/showcase-of-beautiful-typography-done-in-tex-friends