I have a question about the following definition of a continuous preference relation. I apologize for not providing a reference and will try to add one as soon as I can find one.


A preference relation is continuous if for all sequences x_n, y_n with x_n converges to x and y_n converges to y as n goes to infinity and x_n is at least as good as y_n for all n, then this must also hold for the limits x and y.

My simple question is: Is the if an iff or only an if? That is, say this condition (or definition?) above is not ful-filled, can I infer that the preference relation is not continuous or might it still be continuous?


1 Answer 1


This is a definition. Definitions are always iff.

Consider this property. From now on we call this and exactly this (name of the concept here).

  • $\begingroup$ Thank you @denesp. I was not sure if it was a definition or condition. $\endgroup$ Commented Oct 17, 2017 at 7:39
  • 1
    $\begingroup$ @eigenvector That is strange because you yourself wrote "definition" twice. $\endgroup$
    – Giskard
    Commented Oct 17, 2017 at 7:44
  • $\begingroup$ Fair point. Note, though, that I also wrote: "condition (or definition?) once in the last paragraph. Anyway, lets agree that my wording was not very precise. :-) My understanding is still confused. Let me rephrase my question: Is what I wrote above a definition or is it a condition? $\endgroup$ Commented Oct 17, 2017 at 7:59
  • $\begingroup$ @eigenvector As I said in my answer it is the definition. $\endgroup$
    – Giskard
    Commented Oct 17, 2017 at 10:05

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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