This is our monthly thread for collecting arbitrarily contrived scenarios in which somebody gets tortured for 3^^^^^3 years, or an infinite number of people experience an infinite amount of sorrow, or a baby gets eaten by a shark, etc. and which might be handy to link to in one of our discussions. As everyone knows, this is the most rational and non-obnoxious way to think about incentives and disincentives.
Please post all infinite-torture scenarios separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
No more than 5 infinite-torture scenarios per person per monthly thread, please.
This isn't right - aleph numbers are indexed by all ordinals, not just natural numbers. What's equivalent to AC is that the aleph numbers cover all infinite cardinals.
This is our monthly thread for collecting arbitrarily contrived scenarios in which somebody gets tortured for 3^^^^^3 years, or an infinite number of people experience an infinite amount of sorrow, or a baby gets eaten by a shark, etc. and which might be handy to link to in one of our discussions. As everyone knows, this is the most rational and non-obnoxious way to think about incentives and disincentives.