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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: Являeтcя ли вeщeствeнным линeйным прoстрaнcтвoм мнoжecтвo: a) всeх схoдящиxcя пocлeдoвaтeльнoстeй b) всeх рacxoдящиxcя пocлeдoвaтeльнocтeй Можете, пожалуйста, объяснить с помощью примеров?
В частности, множество сходящихся числовых последовательностей также образует линейное пространство, так как сумма двух сходящихся последовательностей сходится, и при умножении всех членов сходящейся последовательности на число получаем сходящуюся последовательность. Напротив, множество расходящихся последовательностей не является линейным пространством, так как, например, сумма расходящихся последовательностей может иметь предел.
В качестве примера того, что сумма двух расходящихся последовательностей может иметь предел, возьмите сумму последовательностей и Получится постоянная последовательность, предел которой равен нулю.
5
Большое спасибо!
Об авторе:
Facta loquuntur.
Форма ответа
Отправка постов/ответов доступна только зарегистрированным и подтвержденным пользователям.
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и 
Получится постоянная последовательность, предел которой равен нулю.