Does the direction/size of a symbol matter if we are writing down the alphabet for a formal language?
What I mean is, we have two formulas, $a<b$ and $b>a$. In that case, is $<$ a different symbol than $>$ and should these two be written as separate symbols in the alphabet.
Or if we have two symbols which mean exactly the same thing, but have different size (e.g. parentheses due to aesthetical reasons), should both of them be written down as separate symbols in the alphabet?
Any of the above matter if you make it matter. You can define your alphabet how you like. If you want to define an alphabet with only $<$ or only $>$ because you can get by with just one, have at it.
Size can matter if you enjoy the benefits of capitalization. $C$ and $c$, $O$ and $o$, $W$ and $w$ are just different sizes for the letters, but one marks the beginning of the first word in a sentence in formal English, and the other doesn't.
But in some cases the size doesn't really change the meaning;
$$[3x^2(3y^2 + z^3)]$$
and
$$\left[3x^2\left(3y^2 + z^3\right)\right]$$
mean the same thing, but one is slightly prettier to look at.