From d73eb4404c66972e7ab33eb04f15cee2b2a29541 Mon Sep 17 00:00:00 2001
From: Konstantin Chukharev <lipen00@gmail.com>
Date: Tue, 1 Oct 2024 10:34:19 +0300
Subject: [PATCH] Add task about well-founded relations

---
 hw2.tex | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/hw2.tex b/hw2.tex
index 1692fe6..6c6e5a6 100644
--- a/hw2.tex
+++ b/hw2.tex
@@ -247,6 +247,11 @@
     Show that the set of all partitions of a set~$S$ with the refinement relation~$\preceq$ is a lattice.
 
 
+    % Task: Well-founded relation.
+    \item A poset $\Pair{R, \preceq}$ is \emph{well-founded} if there is no infinite decreasing sequence of elements in the poset, that is, elements $x_1, x_2, \dots, x_n$ such that $\dots \prec x_n \prec \dots \prec x_2 \prec x_1$.
+    Determine whether the set of strings of lowercase English letters with lexicographic order is well-founded.
+
+
     % \item \dots
 \end{tasks}