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| vicious prophet
Posts: 0 Status: Peasant Karma: 0 [+1] [-1]   |
Subject: answer | |||||
| Infinity is a concept in many fields that refers to a quantity without bound or end. People have developed various ideas throughout history about the nature of infinity. The word comes from the Latin infinitas or "unboundedness.". In mathematics, "infinity" is often treated as if it were a number ( i.e., it counts or measures things: "an infinite number of terms" ) but it is not the same sort of number as the real numbers. The German mathematician Georg Cantor formalized many ideas related to infinity and infinite sets during the late 19th and early 20th centuries. He also discovered that there are different "kinds" of infinite sets, a concept called cardinality. For example, the set of integers is countably infinite, while the set of real numbers is uncountably infinite. A set of elements is Dedekind-infinite if it has a seemingly paradoxical quality: a subset of its elements can be matched up, one-to-one, to all of the elements in the set. The paradoxical nature of infinity is illustrated by the idea of a grand hotel, with infinitely many rooms—all of which are occupied by guests—but can nevertheless manage to accommodate a new guest by moving each existing guest over, one by one, to the next room. This hotel can also hold infinitely more guests by moving guest number one to room number two, guest number two to room four, and moving each guest to the room with double the value. This frees up infinitely more rooms. |
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