Dirichlet Memes

The mathematical flex nobody asked for! This meme showcases the infamous Dirichlet function - the rebel of calculus that equals 1 for irrational numbers and 0 for rational ones. The poor function is literally screaming its values while mathematicians argue about its supremum and infimum (fancy terms for maximum and minimum values). And yet, despite having values of both 0 and 1, this function is so pathologically broken that it can't be integrated using standard methods. It's basically the mathematical equivalent of that friend who technically meets all the requirements for the party but still manages to ruin everyone's night. No wonder calculus professors use it to crush the souls of unsuspecting undergrads!

Ever notice how mathematicians get increasingly dramatic about their weird functions? The Dirichlet function gets a casual "OK" because it's Lebesgue integrable but nowhere continuous—like finding out your date can't swim but makes amazing pasta. Then the Weierstrass function demands attention with its "HOL' UP" because it's continuous everywhere but refuses to be differentiable anywhere—basically the mathematical equivalent of someone who looks perfectly normal but has absolutely no chill. But the Fabius function? That smooth-talking infinitely differentiable yet nowhere analytic tease sends mathematicians into full psychedelic meltdown mode. It's like discovering your calculator has been secretly plotting world domination this whole time. These pathological functions are why math professors drink.