How does one teach uniform continuity?

6 days ago

Yesterday I was teaching my class in infinitesimal differential geometry, by introducing various preliminaries on infinitesimals, including discussion of continuity and uniform continuity. A very bright student in the class saw the hyperreal definition of uniform continuity and exclaimed: "I never understood this stuff until I saw the infinitesimal definition!" Have any of you had similar experiences with infinitesimals?