From 6575aa80f9ad1dd9e0a2f5d1ffab7bdbec30b65a Mon Sep 17 00:00:00 2001 From: Luc Date: Sat, 30 Dec 2023 20:54:26 +0100 Subject: [PATCH] Removed errors. --- config/en/mkdocs.yaml | 2 +- docs/en/mathematics/set-theory/orders.md | 2 ++ 2 files changed, 3 insertions(+), 1 deletion(-) diff --git a/config/en/mkdocs.yaml b/config/en/mkdocs.yaml index 91d679c..fe34ae4 100755 --- a/config/en/mkdocs.yaml +++ b/config/en/mkdocs.yaml @@ -72,7 +72,7 @@ nav: - 'Maps': mathematics/set-theory/maps.md - 'Permutations': mathematics/set-theory/permutations.md - 'Orders': mathematics/set-theory/orders.md - - 'Recursion and induction': mathematics/set-theory/recusrion-induction.md + - 'Recursion and induction': mathematics/set-theory/recursion-induction.md - 'Cardinalities': mathematics/set-theory/cardinalities.md - 'Additional axioms': mathematics/set-theory/additional-axioms.md - 'Calculus': diff --git a/docs/en/mathematics/set-theory/orders.md b/docs/en/mathematics/set-theory/orders.md index dc71ee8..6b400a5 100644 --- a/docs/en/mathematics/set-theory/orders.md +++ b/docs/en/mathematics/set-theory/orders.md @@ -22,6 +22,8 @@ If we consider the poset of all subsets of a set $S$ then the empty set $\varnot > *Definition*: if a poset $(P, \sqsubseteq)$ has a minimum $\bot$, then the minimal elements of $P\backslash \{\bot\}$ are called the atoms of $P$. +
+ > *Lemma*: let $(P, \sqsubseteq)$ be a partially ordered set. Then $P$ contains at most one maximum and one minimum. ??? note "*Proof*:"