Interesting Number Paradox
Some numbers have interesting properties.
Some numbers, on the other hand, have no such interesting properties.
Let $s \in U$ be that smallest element.
Then $s$ has an interesting property: it is the smallest uninteresting number.
Thus $s$ is not an element of $U$, but of $I$.
It follows that the smallest element of $U$ is not $s$ but $s'$ where $s' > s$.
But then $s'$ is now the smallest uninteresting number, and therefore interesting.
And so on.
It follows that there are no uninteresting numbers.
This is an antinomy.
The integers in $U$ are defined as uninteresting.
Once $U$ has been defined, redefining $s$ as interesting cannot be done.
Saying that $s$ is interesting because it is the smallest element of $U$ is to say that $U$ is improperly defined.
Ultimately, the point is that $U$ cannot be well-defined.
If $s$ is moved from $U$ to $I$, that which makes it interesting (it being the smallest element of $U$) no longer holds.
$s$ is no longer interesting and so no longer belongs to $I$.
Thus $s$ cannot belong either to $U$ or to $I$ and hence neither $U$ nor $I$ can be defined.