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 issuch that
.