- #1

- 46

- 17

The axiom can be stated as follows: For every nonempty set ##X## and every entire binary relation ##R## on ##X##, there exists a sequence ##(x_n)_{ n \in \mathbb{N} }## in ##X## such that ##x_nRx_{n+1}## for all ##n \in \mathbb{N}##. (Here, an entire binary relation on ##X## is one where for every ##a \in X##, there exists a ##b \in X## such that ##aRb##.)

See Wikipedia: https://en.wikipedia.org/wiki/Axiom_of_dependent_choice

I want to ask here: what is your experience with this axiom? Did you ever use the “Axiom of Dependent Choice”, how and why?