Then there exists an N such that for all n > N
the above fails if x is irrational. See where this takes you.
Yes, I know this part. My trouble is writing the proof or the "explanation" in a right way.
Is the following will consider a mathematical proof:
When x is rational the double limit can be written as:
and if x irrational:
The double limit can be understood like that(?):
when for all , which is equals (the product) to 0.
And what about: