In This World - Problem of the Day

CNN News Clip

"What is there in a vacuum to make one afraid?" said the flea. "There is nothing in it," I said, "and that is what makes one afraid to contemplate it. A person can't think of a place with nothing at all in it without going nutty, and if he tries to think that nothing is something after all, he gets nuttier." "But that is only part of it," retorted the flea. "What about the infinity of the universe?" "Infinity!" said I. "Infinity is an expression of your imagination." Is the infinite plausible? Can you contemplate the vastness of infinity?

This section lays the groundwork for some fundamental concepts in mathematics. Sets are a unifying idea and will lead us to a means of discussing not only the meaning of something with nothing at all in it, but also the meaning of something that is infinite.