Hey everyone,
How would you prove that this function is not continuous in every x != 1:
x-1 +((x-1)^2)*D(x)
D(x) is Dirichlet function.
if x rational -> D(x) = 0
if not -> D(x) = 1
Thanks a lot,
Michael Engslter
Hey everyone,
How would you prove that this function is not continuous in every x != 1:
x-1 +((x-1)^2)*D(x)
D(x) is Dirichlet function.
if x rational -> D(x) = 0
if not -> D(x) = 1
Thanks a lot,
Michael Engslter
There are several different "Dirichlet functions" but I assume you mean the most common, D(x)= 1 if x is rational, 0 otherwise. Given any x, there exist a sequence of rational numbers that converges to it and there exist a sequence of irrational numbers that converges to it. What is the limit of this function as you approach x along either sequence?