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@ -72,7 +72,7 @@ nav:
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- 'Maps': mathematics/set-theory/maps.md
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- 'Maps': mathematics/set-theory/maps.md
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- 'Permutations': mathematics/set-theory/permutations.md
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- 'Permutations': mathematics/set-theory/permutations.md
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- 'Orders': mathematics/set-theory/orders.md
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- 'Orders': mathematics/set-theory/orders.md
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- 'Recursion and induction': mathematics/set-theory/recusrion-induction.md
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- 'Recursion and induction': mathematics/set-theory/recursion-induction.md
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- 'Cardinalities': mathematics/set-theory/cardinalities.md
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- 'Cardinalities': mathematics/set-theory/cardinalities.md
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- 'Additional axioms': mathematics/set-theory/additional-axioms.md
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- 'Additional axioms': mathematics/set-theory/additional-axioms.md
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- 'Calculus':
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- 'Calculus':
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@ -22,6 +22,8 @@ If we consider the poset of all subsets of a set $S$ then the empty set $\varnot
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> *Definition*: if a poset $(P, \sqsubseteq)$ has a minimum $\bot$, then the minimal elements of $P\backslash \{\bot\}$ are called the atoms of $P$.
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> *Definition*: if a poset $(P, \sqsubseteq)$ has a minimum $\bot$, then the minimal elements of $P\backslash \{\bot\}$ are called the atoms of $P$.
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<br>
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> *Lemma*: let $(P, \sqsubseteq)$ be a partially ordered set. Then $P$ contains at most one maximum and one minimum.
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> *Lemma*: let $(P, \sqsubseteq)$ be a partially ordered set. Then $P$ contains at most one maximum and one minimum.
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??? note "*Proof*:"
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??? note "*Proof*:"
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