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Консультация № 191470
13.10.2017, 09:09
0.00 руб.
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Доказать, что множество точек A={(x,y):y=|x+1|, -1≤x≤1} несчетно
Доказать, что множество точек A={(x,y):y=|x+1|, -1≤x≤1} несчетно
Обсуждение
13.10.2017, 21:39
общий
это ответ
Здравствуйте, frolovala25!
Имеем
При
график функции 
совпадает с графиком функции 
(рисунок ниже).
При этом имеет место взаимно однозначное соответствие (биекция) между точками графика функции
(и графика функции 
) и точками несчётного множества 
в чём можно убедиться, например, проведя отрезки, параллельные оси ординат, которые соединяют произвольные точки графика с точками оси абсцисс. В силу этой биекции заданное множество 
точек графика функции тоже является несчётным.
Имеем
При
график функции совпадает с графиком функции (рисунок ниже).При этом имеет место взаимно однозначное соответствие (биекция) между точками графика функции
(и графика функции ) и точками несчётного множества в чём можно убедиться, например, проведя отрезки, параллельные оси ординат, которые соединяют произвольные точки графика с точками оси абсцисс. В силу этой биекции заданное множество точек графика функции тоже является несчётным.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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