I need help with one set theory problem. Let $A$ be set. Proof that $\exists n(|A|=|n|)$($A$ is finite set) $\implies$ exists binary relation $R$ in $A$ such that $<A,R>$ and $<A,R^{-1}>$ are well ordered sets.
2026-03-26 11:17:22.1774523842
If A is a finite set $\implies$ <A,R> and $<A,R^{-1}>$ are well ordered sets.
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Exists n in N with A = { $a_1, a_2,.. a_n$ }.
What do you think about the orders
$a_jR_k$ iff j <= k and R$^{-1}$?