One idea being communicable in multiple different ways is a recurring
phenomenon in mathematics. This talk will explore an accessible example.
Namely, we will discuss three ideas (see below), which on the surface, seem
somewhat different. However, we will reveal that all three communicate
the same basic concept, and justify this with accessible examples.
- A partition of a set is a collection of subsets that is pairwise disjoint:
and whose union is :
- An equivalence relation on a set is a relation that is reflexive,
symmetric, and transitive.
- A surjection is a function whose range is equal to its
codomain. That is such that .