You should be able to solve this.

Create a method to choose a random integer between 0 and infinity such that no integer is more likely to be chosen than any other.

Yes it is possible, I don't care what your probability book says (Notice I didn't even use the word "probability").  You may assume the axiom of choice.

>>62
>"probability" is useless for them.

OP (i.e. me) is relying on a fuzzy definition of "probability" that makes some intuitive sense but can't be expressed in the usual probability space way.  Whether it actually works or not is up for debate.

>it doesn't use the axiom of choice.
>...
>the only place you use it here is in constructing the vitali sets

¬_¬

>...define X = X_1/10 + X_2/10^2 + X_3/10^3.....

I think that's been mentioned at least 5 times so far slready, except with a binary expansion.