Tuple

🅟 Feb 16, 2026

  🅤 Mar 08, 2026

DEF-TUP. Tuple.

  • The ordered pair / 2-tuple / couple of $a$ and $b$, written as $(a,b)$, is the set

    \[\{\{a\},\{a,b\}\}.\]
  • The 3-tuple / triple of $a$, $b$ and $c$ is

    \[(a,b,c) = ((a,b),c).\]
  • 4-tuples / quadruples, 5-tuples / quintuples, etc. are defined analogously.


PROP-TUP.

For any $a_1$, $\cdots$, $a_n$ and $b_1$, $\cdots$, $b_n$ ($n\geq 2$),

\[(a_1,\cdots,a_n) = (b_1,\cdots,b_n) \enspace\lrimp\enspace a_1=b_1\land\cdots\land a_n=b_n.\]