How can I notate the assignment of each variable in a tuple to a specific value?

Question

Assume I have a tuple of variables, i.e. $\mathcal{T} = (x_1,...,x_n)$. Now I would like to assign each of those elements in the tuple to the same value $c$. How I can I denote this in a formally correct way? Maybe using the $\forall$ symbol?

Answer 1

Why not just write $x_i=c$ for all $i$, or, as suggested above, $x_1=\cdots=x_n=c$? You could also write $(x_1,\ldots,x_n)=(c,\ldots,c)$.

If you wanted to use notation alone, you could write $$\forall 1\leq i\leq n:x_i=c$$ or if the range is understood, $$\forall i:x_i=c$$ However it's a bit of a pet peeve of mine when people only use notation like this. Words are often more understandable. If you do use this, use it sparingly, unless you actually are writing formal strings for the purpose of studying them.