The ordered pair $(a,b)$ is defined in formal set theory as the set $\{\{a\},\{a,b\}\}$. Then ordered triples $(a,b,c)$ are defined in this way: $((a,b),c)$. However, can we define ordered triples as the set $\{\{a\},\{a,b\},\{a,b,c\}\}$, and analogously for higher n-tuples. In other words, does such a definition uniquely determine the components of the ordered triple?
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Think about what happens if $a=b=c$. – Alessandro Codenotti Oct 30 '20 at 23:52
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7What about $(2,3,2)$ versus $(2,3,3)$? – Daniel Schepler Oct 30 '20 at 23:55