Andreas Minne: Counterexamples in Mathematics

If the derivative of a function is zero almost everywhere in the interval (0,1), then the function has to be constant there. Actually, this is not true which can be shown by a counterexample to the above statement. This and other perhaps plausible but false mathematical statements will be considered by looking at counterexamples. These are all taken from different fields in mathematics but will mostly revolve around analysis.