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Chapter 2. To infinity --- and Beyond!

Figure A. Gottfried Leibniz (1646-1716)

Little kids readily pick up the idea of infinity. “When I grow up, I'm gonna have a million Barbies.” “Oh yeah? Well, I'm gonna have a billion.” “Well, I'm gonna have infinity Barbies.” “So what? I'll have two infinity of them.” Adults laugh, convinced that infinity, ∞, is the biggest number, so 2∞ can't be any bigger. This is the idea behind a joke in the movie Toy Story. Buzz Lightyear's slogan is “To infinity --- and beyond!” We assume there isn't any beyond. Infinity is supposed to be the biggest there is, so by definition there can't be anything bigger, right?