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Our infinite quest began in the Yahoo! Directory, in a math category called Specific Numbers > Infinity. We stopped in at the Hotel Infinity and learned that infinity "is not a number or a thing, but the idea behind many notions." Finite human experience requires a concept like infinity to account for the fact that you can always keep counting higher, that parallel lines will never meet, no matter how long you draw them, and that if you keep dividing a line of any length in half, there seems to be no end to the number
of times you can divide it. On a site from the University of Toronto, an essay titled "Is there really such a thing as 'infinity'?" made us realize this was going to be tough. Infinity is a concept that only works in certain specific theoretical contexts. In topology, an advanced branch of geometry, a sequence of objects can converge toward infinity. Topology is referred to as "rubber sheet geometry," because it studies the geometric patterns and relative positions of hypothetical figures that can be bent, twisted, or stretched. A non-mathematician might have difficulty distinguishing the sense from the nonsense in a topologic space. In
set theory, the idea of infinity comes in handy. Sets describe collections of real or conceptual entities. The natural numbers (1,2,3,4...) can be used to measure finite sets, but to measure infinite sets, you need to use infinite cardinal numbers, and guess what? "There are in fact infinitely many different infinite cardinal numbers!" A philosophical work-in-progress called Principia Cybernetica distinguishes between potential infinity, as exemplified by endless processes (like counting), and actual infinity, an infinitely less useful concept for systems scientists and computer programmers. Although
infinity may be intriguing to children and mathematicians, it is, nonetheless, a "deep and confounding" idea.
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