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.)
… is the square root function.
Why? It’s a perfect example of a function that many people think is well defined, but in reality is not. Continue reading
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?