When things are similar but aren’t equal

Or when we need to order things, relations are a flexible mathematical notion that allows us to compare terms or elements.

The most familiar relation is equality. But you have encountered many others at this point:

• $ \to $ - implication of propositions
• $ \leq $ - less than (or equality) of numbers
• $ \subseteq $ - subset containment
• $\mid$ - divisibility

Relations unify all these concepts. We will discuss the general concept and then branch off to investigate different common properties of relations.

Table of contents

• Basic ideas
• Useful properties
• Partial and total orders
• Equivalence relations