Today we’ll talk about some paradoxical things, like the logarithm of zero, and the maximum element of a set of real numbers that doesn’t contain any real numbers at all. More importantly, we’ll see how mathematicians try to wrap their heads around such enigmas.

All today’s logarithms will be base ten logarithms; so the logarithm of 100 is 2 (because 100 is 10^{2}) and the logarithm of 1/1000 is −3 (because 1/1000 is 10^{−3})). The logarithm of 0 would have to be an *x* that satisfies the equation 10^{x} = 0. Since there’s no such number, we could just say “log 0 is undefined” and walk away, with our consciences clear and our complacency unruffled.

**BUT WE AREN’T GOING TO DO THAT, ARE WE?**