Is there a reason, why the set of polynomials of, say, a field is sometimes written as $K[X]$ and sometimes as $K[x]$, i.e. is there a reason, why the "indeterminate" is sometimes denoted with $x$ and sometimes with $X$ ?
(I'm thinking, perhaps in some areas of math/for some fields, $x$ is preferred to $X$ to maybe pronounce the fact that the formal polynomials $\sum_i a_i x^i$ correspond one-to-one to functions $f(x)=\sum_i a_i x^i$ (since if the indeterminate is denoted with $x$, there is no notational difference to the notation of a function), whereas the notation $\sum_i a_i X^i$ would maybe suggest that this correspondence isn't one-one ? )