$\"\"$

The function is $\"\"$ .

Consider $\"\"$ ,

if for every number of $\"\"$ , there exists a $\"\"$ such number $\"\"$ whenever $\"\"$ .

Consider $\"\"$ .

If $\"\"$ is rational the function value is $\"\"$ .

$\"\"$

If $\"\"$ is irrational the function value is $\"\"$ .

$\"\"$

The value of the function is not approaching to a unique value.

$\"\"$ does not exist.

$\"\"$

$\"\"$ does not exist.