Thomae's function is a real-valued function of a real variable that can be defined as:
is continuous at all irrational numbers. But, is discontinuous at all rational numbers.
It is interesting to note that there doesn't exist any function that is continuous only at the rational points.WHY?
Suppose such a function exists, then can be written as a countable union of nowhere dense sets, contradicting the Baire category theorem.
Comments
Post a Comment