- #1

steenis

- 312

- 18

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?