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Mostly I've seen people use the following notation: If $s=(3,\emptyset, i)$ is some arbitrary tuple, then we have $s_1=3, s_2=\emptyset$ and so forth. However, sometimes in a tuple, the different entries have distinct ideas belonging to them and it makes sense to give them names instead, meaning, to write $s_n=3,s_{set}=\emptyset,s_c=i$ instead of $s_1=3, s_2=\emptyset$. I'm tempted to write something like $s\in (n\in \mathbb N)\times (set \in \mathcal P(N))\times (c\in \mathbb C)$, so that $s_n=3,s_{set}=\emptyset,s_c=i$. Is there a standard notation along these lines?

user56834
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    You could write $s=(3,\emptyset,i)\in\Bbb N\times \mathcal P(\mathbb N)\times \mathbb C$ – J. W. Tanner Jan 17 '21 at 16:05
  • @J.W.Tanner, I maybe should rephrase the question. – user56834 Jan 17 '21 at 17:03
  • I'm not sure @J.W.Tanner was providing an answer in a comment, so much as correcting the nonstandard "$(n\in\mathbb N)\times(set\in\mathcal{P}(N))\times(c\in\mathbb C)$". Though I'm not sure since the use of the word "could" is suggestive. – Mark S. Jan 17 '21 at 17:16
  • I don't think there's anything "standard" on this matter, because I can't see the usefulness of having tuples with items from different sets in them. – K.defaoite Jan 17 '21 at 17:19
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    @K.defaoite A pointed space is an example. There are many examples. – user56834 Jan 17 '21 at 17:27

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