There are a couple constructions like this in mathematics that... really make you think. Like Banach Tarski doesn’t make any sense.

Or the one that still bothers me, ten years after I learned it. Is take an enumeration of the rationals and take the union of balls of with radius epsilon/2^n over this enumeration. And you can create dense open subsets of the real numbers, that miss basically every real number. Despite containing an open interval around every rational. The conclusion I’ve come to is the real numbers don’t make any sense.