Math Help - dirichlets function

1. dirichlets function

prove that dirichlets function (nowhere continuous function on [0,1]) is not of bounded variation.

2. If a function is of bounded variation then it is the difference of two monotone functions and is therefore continuous almost everywhere. You will find a bit more detail about those assertions and their proofs here.

3. dirichlets function

how can i show that dirichlets function can not be expressed as the diffrence of two increasing functions?

4. Originally Posted by Kat-M
how can i show that dirichlets function can not be expressed as the diffrence of two increasing functions?
That's because the difference of two increasing functions would have to be continuous except at countably many points (see Monotonic function - Wikipedia, the free encyclopedia).