# How can you tell if any given preference structure is continuous or not?

From a given preference structure (not the utility function), how can one tell if it satisfies the continuity axiom of preferences?

• Can you elicit preferences on infinitely many pairs of bundles of your choosing? That is, for any two bundles A and B, can you always elicit which one the household prefers? – BKay Oct 6 '15 at 13:19

By trying to prove whether the following holds.

Note: Image taken from http://www.econ.ucla.edu/iobara/lecturepreferenceandutility201a.pdf

• note: I was being sarcastic. – ramazan Oct 6 '15 at 6:07