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In mathematics, the real line, or real number line is the line whose points are the real numbers. That is, the real line is the set of all real numbers, viewed as a geometric space, namely the Euclidean space of dimension one. It can be thought of as a vector space (or affine space), a metric space, a topological space, a measure space, or a linear continuum. Just like the set of real numbers, the real line is usually denoted by the symbol (or alternatively, , the letter “R” in blackboard bold). However, it is sometimes denoted in order to emphasize its role as the first Euclidean space. This article focuses on the aspects of as a geometric space in topology, geometry, and real analysis. The real numbers also play an important role in algebra as a field, but in this context is rarely referred to as a line. For more information on in all of its guises, see real number. ==As a linear continuum== The real line is a linear continuum under the standard ordering. Specifically, the real line is linearly ordered by , and this ordering is dense and has the least-upper-bound property. In addition to the above properties, the real line has no maximum or minimum element. It also has a countable dense subset, namely the set of rational numbers. It is a theorem that any linear continuum with a countable dense subset and no maximum or minimum element is order-isomorphic to the real line. The real line also satisfies the countable chain condition: every collection of mutually disjoint, nonempty open intervals in is countable. In order theory, the famous Suslin problem asks whether every linear continuum satisfying the countable chain condition that has no maximum or minimum element is necessarily order-isomorphic to . This statement has been shown to be independent of the standard axiomatic system of set theory known as ZFC. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Real line」の詳細全文を読む スポンサード リンク
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