Canvas: Popcorn Function

Description

In real analysis, students see “pathological” functions, such as the popcorn function, which takes the value 1/q at p/q in lowest terms and is 0 otherwise.

The popcorn function has surprising properties that test students’ facility with the definitions of real analysis. Its limit is 0 at every real number, hence is continuous at every irrational number and discontinuous at every rational. Despite having infinitely many discontinuities, however, this function is integrable over an arbitrary interval, with integral is 0.

EU representative: HONSON VENTURES LIMITED, gpsr@honsonventures.com, 3, Gnaftis House flat 102, Limassol, Mesa Geitonia, 4003, CY

Product information: Generic brand, 2 year warranty in EU and Northern Ireland as per Directive 1999/44/EC

Care instructions: If the canvas does gather any dust, you may wipe it off gently with a clean, damp cloth.