When $X$ is a set, we can write:
for all $x\in X$ …
But say that $X=(a, b, c, … ,n)$. I.e. an ordered tuple.
Is it standard notation to still say the following?
for all $x\in X$…
It might be confusing because if you interpret it as a sentence in ZFC, then you're not quantifying over the thing you want (you're including the sets representing the order). But how would we write down to quantify over just the elements of the tuple?
Best Answer
I've seen it written as you wrote it, numerous times. Sometimes conciseness yields better clarity than perfect rigour.
An alternative is to write the elements of the $t-$uple in an "indexed" form such as $a_1,\dots,a_t$, and then quantify over the range of indices ("$\forall i$ ... $a_i$ ...").