I am not sure about this nested limit, but we get the Dirichlet function if we swap limits:
.
If x is rational, then m!x is eventually an (even) integer. If x is irrational, then , so the inner limit is 0.
I am not sure about this nested limit, but we get the Dirichlet function if we swap limits:
.
If x is rational, then m!x is eventually an (even) integer. If x is irrational, then , so the inner limit is 0.