An Everywhere Continuous Nowhere Differentiable Function, interesting proof by John McCarthy

[hhm]

http://www-formal.stanford.edu/jmc/weierstrass/weierstrass.html

[pfedor]

Another funny excercise: Find a function which is continuous at all irrational numbers and non-continuous at all rational numbers.

[kurtosis]

Nice - the proof that almost all Brownian motion paths have this property is much uglier