EDB — 02K

[02K] Attention! Suppose as above that the sets \(A_ i\) are not empty. This is formally written as \(∀ i∈ I,∃ x∈ A_ i\). Intuitively this brings us to say that the element \(x\) depends on \(i\), and therefore that \(x=x(i)\). This step, as intuitive as it is, is exactly the axiom of choice.