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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?

Chris
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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.

Matt Samuel
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  • True, I could do that, but I don't think its nice. I thought more about something like: $\forall x_i \in \mathcal{T}: x_i = c$ but I don't know if that is correct formally. – Chris Jan 21 '19 at 13:15
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    @Chris I would avoid using notation like that unless it's absolutely necessary. It's hard to read. – Matt Samuel Jan 21 '19 at 13:16
  • @Chris I put in two examples of doing it the way you suggest. – Matt Samuel Jan 21 '19 at 13:20
  • thanks! I agree that the most simple notation which transports the same message is probably the cleanest way. But besides that, was my proposed solution correct from a formal point of view? – Chris Jan 21 '19 at 13:22
  • @Chris Yes. You could quantify over the set or over the index. – Matt Samuel Jan 21 '19 at 13:22