Mode of a Uniform Distribution

Hi Folks,

I searched for this (google, wiki, Talk Stats) and didn't find the response (which doesn't mean it's not there somewhere but...).

Looking at the definition for Mode it seems to leave the door open to the mode of a uniform distribution being multimodal containing all of the data points, as long as they occur more than once (according to a 9th grade math book).

I found a discussion on "The Math Forum"

where it seems as though this question has a legitimate concern regarding interpretation of the definition.

Is there a "STANDARD" definition of Mode that solves this without any hint of ambiguity.

thank you for taking a noob Q.