@noelle The key in breaking this proof is in understanding that "interesting" is not a discrete property but rather a continuous one. this is even reflected in your own language about how there is a most and least, explicitly stating they are sortable at a minimum, and implying they are continuous.
Therefore the least interesting of all the interesting numbers would be more interesting than the most interesting of the not interesting numbers. and that this logic can be carried out recursively ad infinitum. Things break down quickly after this :)