I'm just getting into Vi Hart's animated presentations. I would not recommend them over hard work doing your own mathematics, but to whet your appetite here's an elegant proof that some infinities are bigger than others.
I don't recommend her musical tastes.
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"And if we have unearned luck, now to scape the serpent's tongue, we will make amends ere long. Else the Puck a liar call ..."
So speak.