Does Infinity Come in Different Sizes?

摘要

In the 1995 film Toy Story, the gung-ho space action figure Buzz Lightyear tirelessly incants his catchphrase: "To infinity... and beyond!" The joke, of course, is rooted in the perfectly reasonable assumption that infinity is the unsurpassable absolute—that there is no beyond. That assumption, however, is not entirely sound. As German mathematician Georg Cantor demonstrated in the late 19th century, a variety of infinities exist—and they can be classified by their relative sizes.