@jbrocollins why didn't we cover this last semester?
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Take a curve with infinite length but finite area underneath like e^{-x} for 1<x. Rotate it about the x-axis. Covered.
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this is how black holes exist, packing infinite curvature of spacetime into finite volume
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Or the easier to grasp Koch snowflake - with finite area but infinite circumference.
@fermatslibrarypic.twitter.com/G8Vkonp5Mg
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it is open, how can it have volume?

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Sum of 1/n^2 converges but you still keep adding infinite numbers
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You can fill it with paint, but you can't fully paint its inside!
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If filled with paint it won't be enough to paint either the outside or the inside
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@amorechka that's what she saidThanks. Twitter will use this to make your timeline better. UndoUndo
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