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In Wikipedia, one formulation of the Axiom of Choice states the following:

Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

I'm somewhat confused by this statement. For suppose $X=\{\{1\}, \{2\}, \{3\}\}$. What would the set $C$ be in this case?

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$C=\{1,2,3\}$ will do. It has one element in common with each of the sets in $X$ (it has $1$ in common with $\{1\}$; it has $2$ in common with $\{2\}$, and $3$ with $\{3\}$)

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  • $\begingroup$ I see. I thought "exactly one element" means a set of exactly one element. $\endgroup$ – sequence Sep 13 '17 at 3:47

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