1

Prove that the following statements are equivalent.

1-) The Cartesian product of a non-empty family of non-empty sets is also non-empty, i.e, $\{A_i: i \in I\}, I\neq \emptyset, A_i \neq \emptyset \Rightarrow \Pi _{i \in I} A_i \neq \emptyset$

2-) all non-empty collection of non-empty sets admits function choice, i.e, $\tau \neq \emptyset , \forall A \in \tau , A \neq \emptyset \Rightarrow \exists f:\tau \to \bigcup \{A: A \in \tau\}$ where $A \to f(A) \in A$

I can not get started

Asaf Karagila
  • 393,674
Lucas
  • 1,319
  • 1
    That is the definition of a product of sets being non-empty. – Asaf Karagila Apr 12 '19 at 18:14
  • Try to put more effort into searching and into your questions than just writing it out. If you can't get started, start by writing out the definitions of your assumption, and the definition that you need to verify. – Asaf Karagila Apr 12 '19 at 18:16
  • It might help to write $\tau$ as $\tau={A_i \mid i\in I}$. – kccu Apr 12 '19 at 18:17

0 Answers0