Would the real imaginary number please stand up?

Well, you’ve may have heard about imaginary numbers. There’s one problem: They don’t exist. Not really. That’s why they are called imaginary numbers. Real numbers, by contrast, do exist. You can put your hand on 2 apples. You can’t put your hand on an imaginary number of apples (unless you’ve had some mind-altering drugs, but that’s another story altogether.)

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To Infinity (and beyond!)

Infinity is not an intuitive concept for most people. My favorite example is the magician with the inifinite hat:

Boffo the Impossible has an amazing trick. Starting at 11:00 am, Boffo puts two balls into a hat, and pulls one out. Every time he gets half-way closer to noon, he puts two balls in, and takes one out. So, at 11:30, he puts two in and takes one out. At 11:45, he puts two in and takes one out. At 11:52:30, he puts two in and takes one out. And so on — he becomes an flurry of activity as he gets closer to noon. At noon, he stops.

The question is: how many balls are left in his hat at 12:01 pm?

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