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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 bothe
by hilbertseries 6y ago
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.
- Dylan16807 6y ago> The conclusion I’ve come to is the real numbers don’t make any sense. Oh they definitely don't. Almost all real numbers are uncomputable, which means they cannot be written down or communicated in any way.
- sukilot 6y agoReal numbers aren't real. Imaginary numbers aren't imaginary. Infinities are unphysical, so you can understand them by analogy to anything that exists in the real Universe.