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}

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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}

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For (a) , for example , the minimal element of wrt the usual order

on the natural numbers.

You try now the other ones by yourself.

Tonio