The set of all real numbers is called a continuous set number, and a set that has continuous set numbers is called a continuum. For example, the set of all points on a line, the set of all points on a plane, and the set of all points in space are all continua. Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information |
実数全体の集合の集合数を連続集合数といい,連続集合数をもつ集合を連続体という。たとえば,直線上の点全体のつくる集合,平面上の点全体のつくる集合,空間の点全体のつくる集合は,いずれも連続体である。
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