The function x²ⁿ + y²ⁿ = 1 is the unit-circle for n=1, but approaches the unit-square as n→∞pic.twitter.com/AVx8wt8XaY
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Here's the proof. When n is large, then x²ⁿ≈0 and y²ⁿ≈0 for all |x|,|y|<1. So everything not strictly equal to 1 will get mapped to 0, as n→∞. Therefore the the limiting solutions to x²ⁿ + y²ⁿ = 1 are (±1,y) with |y|<1 (x, ±1) with |x|<1 QED
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sorry! i didn't mean unit-square! just.. a square with area 4
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I love how you can tell if someone is a mathematician or a physicist based on how they prove things.
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