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In real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extension of the set of the real numbers, by a point denoted ∞. It is thus the set with the standard arithmetic operations extended where possible, and is sometimes denoted by The added point is called the point at infinity, because it is considered as a neighbour of both ends of the real line. More precisely, the point at infinity is the limit of every sequence of real numbers whose absolute values are increasing and unbounded.

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  • Projectively extended real line
  • Reta real estendida projetivamente
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  • In real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extension of the set of the real numbers, by a point denoted ∞. It is thus the set with the standard arithmetic operations extended where possible, and is sometimes denoted by The added point is called the point at infinity, because it is considered as a neighbour of both ends of the real line. More precisely, the point at infinity is the limit of every sequence of real numbers whose absolute values are increasing and unbounded.
  • Na análise real, a reta real estendida projetivamente (também chamada de compactificação com um ponto da reta real), é a extensão da reta numérica por um ponto indicado ∞. É, portanto, o conjunto (em que é o conjunto dos números reais) com as operações aritméticas usuais estendidas estendido sempre que possível, e às vezes denotado por O ponto adicionado é chamado de ponto no infinito, porque ele é considerado como um vizinho de ambas as extremidades da reta real. Mais precisamente, o ponto no infinito é o limite de toda sequência de números reais cujos valores absolutos são crescentes e ilimitados.
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  • In real analysis, the projectively extended real line (also called the one-point compactification of the real line), is the extension of the set of the real numbers, by a point denoted ∞. It is thus the set with the standard arithmetic operations extended where possible, and is sometimes denoted by The added point is called the point at infinity, because it is considered as a neighbour of both ends of the real line. More precisely, the point at infinity is the limit of every sequence of real numbers whose absolute values are increasing and unbounded. The projectively extended real line may be identified with the projective line over the reals in which three points have been assigned specific values (e.g. 0, 1 and ∞). The projectively extended real line must not be confused with the extended real number line, in which +∞ and −∞ are distinct.
  • Na análise real, a reta real estendida projetivamente (também chamada de compactificação com um ponto da reta real), é a extensão da reta numérica por um ponto indicado ∞. É, portanto, o conjunto (em que é o conjunto dos números reais) com as operações aritméticas usuais estendidas estendido sempre que possível, e às vezes denotado por O ponto adicionado é chamado de ponto no infinito, porque ele é considerado como um vizinho de ambas as extremidades da reta real. Mais precisamente, o ponto no infinito é o limite de toda sequência de números reais cujos valores absolutos são crescentes e ilimitados. A reta real estendida projetivamente pode ser identificada com a reta projetiva sobre os reais em que foram atribuídos valores específicos três pontos (e.g. 0, 1 e ∞). A reta real estendida projetivamente não deve ser confundida com a reta numérica real estendida, em que +∞ e −∞ são distintos.
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