Content-Type: text/shitpost

Today I spent like ten minutes trying to think whether it was possible to find a subset of the real line that could be partitioned into an uncountable family of (nontrivial) intervals.

The answer is no, but it should have taken me way less than ten minutes to think of why. Each interval contains at least one rational number. Since the intervals are disjoint, there are not enough rational numbers to go around.