Disagreeing Functions
A couple of functions bicker: g agrees with f(x) = 0 almost everywhere (on the irrationals), disagreeing only on the rationals, a set of measure zero.
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Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2025-06-26-disagreeing-functions/ (CC BY-NC 4.0)Transcript
[1] f(x) = 0: "Why do you never agree with me?" g(x) = {1, x rational; 0, x irrational}: "Babe, I almost *always* agree with you."
[2] f: "YOU'RE DISAGREEING WITH ME RIGHT NOW" g: "Babe, it's only *interesting* when we disagree."