>>38
You don't need AC to pick an element from one infinite set.
The problem was to pick an element uniformly at random from the integers (a countable set) which is the same thing as picking an element at random from the set of sequences of coinflips that are eventually all zero, since the two sets are in bijection.
God damnit. YOU brought up this representation of the question fuckhat, not me. I didn't say shit about sequences. YOU rephrased the question, then accused me of having done it, and then said it wasn't useful, and then accused me of using AC to wave it away.
I don't disagree that YOUR sequence representation is not useful. THAT'S WHY I DIDN'T FUCKING SAY IT!
Fucking listen. MY statement is that picking an element uniformly at random from the integers is the same as picking a random integer from a finite set an infinite number of times by construction via decimal representation. In other words I have an INFINITE number of bins (countably many numbered 0 and up), each containing a FINITE set. AC allows me to choose an element from EACH BIN, even though there are infinitely many. I can certainly choose an element from ONE BIN uniformly randomly since it has finite contents. Therefore it is possible to choose uniformly randomly one element from each bin. Using this as the decimal representation of the number, I get a uniformly randomly generated finite number between zero and infinity.
Notice I didn't say fuck all about sequences? It's not a fucking goddamn sequence. THIS HAS NOTHING TO DO WITH SEQUENCES.
Notice how
>>16 and
>>40 both agree that infinite coinflips are implicitly valid by the assumption of AC. The reason you're thinking of it as a sequence is because you can't wrap your head around the concept of 'infinite bins' or 'infinite coinflips'. Well guess what, you've successfully stumbled onto the controversial aspect of AC. Congratulations for demonstrating to the rest of the class.