I have a notational question.
In a formal proof, suppose I'm making some statements about a finite set $B$, such that $|B| = n$, for some $n \geq 3$, $n$ belonging to the naturals.
Supposed that in some part of the proof, I must write the subset (or the set itself) as $\{x^n, x^{n-1},..., x^{j+1}, x^j\}$ to make a statement. Even though I'm technically saying the set has more than 3 elements, my statement would still work if $n=3$, by ignoring the elements $x^{n-2}, ..., x^{j+1}$, as if $n = 3$ and $j = 1$.
Is it technically wrong to write the set like that?
That notation is standard, it just gives you a better idea of how the set is built when $n$ is sufficiently large, but it's understood that you're not implying that the set has more than 3 elements.