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 Jul 25 awarded Editor Jul 25 revised Formalization of n-ary functions General formatting Jul 25 comment Formalization of n-ary functions I think the idea of clone is quite interesting. However, using clones pre-supposes a formalization of $n$-ary functions, so I'm not sure how this applies to my question. Jul 25 awarded Scholar Jul 25 accepted Formalization of n-ary functions Jul 25 comment Formalization of n-ary functions Also, if $f$ really is unary, this definition boils down to the usual. Awesome! Jul 25 comment Formalization of n-ary functions @Sridhar: Why did you not make that an answer? It looks like a great idea! Jul 25 comment Formalization of n-ary functions Thanks for the answer. I like the way in which you define tuples. I been born and raised to defined $n+1$-tuples as $(a_1, a_2, \dots, a_{n+1}) = (a_1, (a_2, \dots, a_{n_1}))$, so thinking of treating them differently didn't really enter my head. If tuples are defined as you show, then $f$ doesn't just "feel", $n$-ary, I think it can truly be called $n$-ary. Jul 25 asked Formalization of n-ary functions