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Sorting Socks: A Binary Relation Approach

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  1. Sorting Socks

  2. Sort these 6 socks • How to determine which comes first?

  3. Compare 2 at a time • Draw arrows froman “earlier” sock toa “later” one. • As many arrows as you wish to show the sorting order you have decided.

  4. Sorting as a Binary Relation

  5. Sorting as a Binary Relation You don’t want Symmetry

  6. Sorting as a Binary Relation This sort of Symmetry is ok though

  7. Sorting as a Binary Relation We want self loops

  8. Sorting as a Binary Relation

  9. Sorting as a Binary Relation We want Transitivity

  10. Sorting as a Binary Relation With these properties: • Reflexive • Anti-symmetric • Transitive A binary relation with said properties is called a partial order. Sorting requires at least a partial order; better still a total order.

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