# Choice functions for collections...

• Feb 18th 2011, 10:23 AM
iamthemanyes
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}
• Feb 18th 2011, 03:37 PM
tonio
Quote:

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