On: Two envelopes problem

[dllthomas]

We're not dealing with the natural numbers, right? Otherwise, you obviously want to open the envelope and always switch when you see an odd number.

Of course, the lack of a uniform distribution on the reals or rationals presents the same problem.

[eru → dllthomas]

> We're not dealing with the natural numbers, right?

Well, you can either assume that the envelope's numbers are specified only up to pennies. Or you can just round and say you don't care about sub-pennies.

Or you can go with your suggestion, and look at the lack of a uniform distribution over the reals / rationals.