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Thomae's function, also called the "popcorn function". It's continuous at all irrationals and discontinuous at all rationals. Here a picture:
Thomae's function http://upload.wikimedia.org/wikipedia/commons/thumb/1/15/Thomae_function_(0,1).svg/200px-Thomae_function_(0,1).svg.png
Thomae's functionThomae's function, oralso called the popcorn function"popcorn function". It's continuous at all irrationals and discontinuous at all rationals. http://en.wikipedia.org/wiki/Thomae%27s_function Here a picture:
Thomae's function, or the popcorn function. It's continuous at all irrationals and discontinuous at all rationals. http://en.wikipedia.org/wiki/Thomae%27s_function