Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

At the end of Diamond's Evaluation of Infinite Utility Streams he proves a theorem (which he doesn't give a name to, but it's at the very end of the article). There is a step in which he jumps from $(u,0)_{rep}\succ (0,u)_{rep}$ to $(u,0)\succ_t (0,u)$, and I don't understand where that comes from. It seems like it's the opposite direction of axiom A2, and I don't see how that's derived.

share|cite|improve this question
up vote 1 down vote accepted

Step: $(u,0)_{rep}\succ (0,u)_{rep}\implies (u,0)\succ_2(0,u)$

Proof: Suppose not. Since $\succeq_2$ is complete, we would have $(0,u)\succeq_2 (u,0)$ otherwise, and hence by A2 $(0,u)_{rep}\succeq (u,0)_{rep}$. This cannot be.

I don't see how the rest of Diamond's proof works out though. $(u,0,U)\succeq(0,u,U)$ follows now from A1, but I don't see why this should be strict.

share|cite|improve this answer
Good point. But adding a strict variant of (A1) doesn't seem remarkably controversial, relative to the other axioms. – Xodarap Oct 26 '12 at 0:24
@Xodarap It isn't, but I'm a sucker for minimalism. Thanks for the bounty! – Michael Greinecker Oct 26 '12 at 0:36

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.