Anki Deck Changes

Commit: cde44b4f - lex order fix - thanks jonas :)

Author: obrhubr <obrhubr@gmail.com>

Date: 2025-12-30T12:21:51+01:00

Changes: 1 note(s) changed (0 added, 1 modified, 0 deleted)

Note 1: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Classic
GUID: tBd|.5x#E:
modified

Before

Front

ETH::1._Semester::DiskMat::3._Sets,_Relations,_and_Functions::5._Partial_Order_Relations::3._Combinations_of_Posets_and_the_Lexicographic_Order
How is the lexicographic order \(\leq_{\text{lex}}\) on \(A \times B\) defined?

Back

ETH::1._Semester::DiskMat::3._Sets,_Relations,_and_Functions::5._Partial_Order_Relations::3._Combinations_of_Posets_and_the_Lexicographic_Order
How is the lexicographic order \(\leq_{\text{lex}}\) on \(A \times B\) defined?
\[(a_1, b_1) \leq_{\text{lex}} (a_2, b_2) \overset{\text{def}}{\Longleftrightarrow} a_1 \preceq a_2 \lor (a_1 = a_2 \land b_1 \sqsubseteq b_2)\]

After

Front

ETH::1._Semester::DiskMat::3._Sets,_Relations,_and_Functions::5._Partial_Order_Relations::3._Combinations_of_Posets_and_the_Lexicographic_Order
How is the lexicographic order \(\leq_{\text{lex}}\) on \(A \times B\) defined?

Back

ETH::1._Semester::DiskMat::3._Sets,_Relations,_and_Functions::5._Partial_Order_Relations::3._Combinations_of_Posets_and_the_Lexicographic_Order
How is the lexicographic order \(\leq_{\text{lex}}\) on \(A \times B\) defined?
\[(a_1, b_1) \leq_{\text{lex}} (a_2, b_2) \overset{\text{def}}{\Longleftrightarrow} a_1 \prec a_2 \lor (a_1 = a_2 \land b_1 \sqsubseteq b_2)\]
Field-by-field Comparison
Field Before After
Back \[(a_1, b_1) \leq_{\text{lex}} (a_2, b_2) \overset{\text{def}}{\Longleftrightarrow} a_1 \preceq a_2 \lor (a_1 = a_2 \land b_1 \sqsubseteq b_2)\] \[(a_1, b_1) \leq_{\text{lex}} (a_2, b_2) \overset{\text{def}}{\Longleftrightarrow} a_1 \prec a_2 \lor (a_1 = a_2 \land b_1 \sqsubseteq b_2)\]
Tags: ETH::1._Semester::DiskMat::3._Sets,_Relations,_and_Functions::5._Partial_Order_Relations::3._Combinations_of_Posets_and_the_Lexicographic_Order
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