Prove the following:

and show that:

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- May 25th 2011, 09:56 AMAlso sprach ZarathustraDouble limit.
Prove the following:

and show that:

- May 25th 2011, 10:06 AMTheEmptySet
Hint if

Then there exists an N such that for all n > N

the above fails if x is irrational. See where this takes you. - May 25th 2011, 12:26 PMAlso sprach Zarathustra

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:

or:

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:

Thank you!