How to refer to the single element inside a unit set?

Question

The other similr questions/answers refer to advanced set theory notation or defining exclusive functions for this. [I have answered here my own question with a middle ground solution.]

If sets were ordered, I could just do $s_1$ and get the first, also only element of the unit set $s$. But they are not ordered. Is there a shorthand for that?

Related: how to extract an element according to a single-match criterion, like pertaining to another set?

What is a "unitary set"? Is that that a set of one element, i.e. a singleton? — Ben Grossmann, Jun 25 '20 at 16:50
By definition $\bigcup{s}=s$, though I suspect that only folks with some significant background in set theory will be familiar with the fact. — Brian M. Scott, Jun 25 '20 at 16:54
@lemontree I am a bit confused about needing a \phi to use the \iota thing. — dawid, Jun 25 '20 at 17:05
The $\iota$ operator works on a statement, which is what $\phi$ stands for. In your case, the statement is "is an element of $s$". So: "the s" = $\iota x (x \in s)$. Probably readers familiar with the $\iota$ operator would also understand what you mean if you just write $\iota s$. — Natalie Clarius, Jun 25 '20 at 17:19
@lemontree Ok, I think I can use the shorter form of iota and explain in text at the first time. — dawid, Jun 25 '20 at 17:24

score 1 · Accepted Answer · answered Jun 25 '20 at 17:08

1

Based on parts of answers pointed by the comments, I think a good approach would be $[\{x\} \mapsto x](s)$.

answered Jun 25 '20 at 17:08

dawid

333

How to refer to the single element inside a unit set?

1 Answers1