# Thread: Choice functions for collections...

1. ## Choice functions for collections...

Find if possible a choice function for each of the following collections, without using the choice axiom:

a. The collection A of nonempty subsets of Z+ (positive integers)
b. The collection B of nonempty subsets of Z (integers)
c. The collection C of nonempty subsets of the rational numbers Q
d. The collection D of nonempty subsets of X^(omega), where X = {0, 1}

2. Originally Posted by iamthemanyes
Find if possible a choice function for each of the following collections, without using the choice axiom:

a. The collection A of nonempty subsets of Z+ (positive integers)
b. The collection B of nonempty subsets of Z (integers)
c. The collection C of nonempty subsets of the rational numbers Q
d. The collection D of nonempty subsets of X^(omega), where X = {0, 1}

For (a) , for example , $\displaystyle \forall\,X\in A\,,\,\,f(X):=$ the minimal element of $\displaystyle X$ wrt the usual order

on the natural numbers.

You try now the other ones by yourself.

Tonio