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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
1) Пусть A = {2,3,4}, B = {4,5,6,9,12,16}. Опишите с помощью графа и таблицы отношение xRy[$8660$]x [$8712$] A; y = 3x - 2; 2) Используя понятие мощности конечного множества, равномощности, решить задачу на доказательство. Показать, что если А и В бесконечны и A включает B то А и В, могут быть равномощными в смысле возможности взаимно однозначного со-ответствия элементов множеств. 3)Доказать, что: А [$8745$] В включает С [$8660$] А включает [$172$]В [$8746$] С.
2) Используя понятие мощности конечного множества, равномощности, решить задачу на доказательство. Показать, что если А и В бесконечны и A включает B то А и В, могут быть равномощными в смысле возможности взаимно однозначного соответствия элементов множеств.
Чтобы показать требуемое, рассмотрим множество натуральных чисел (которое будем считать множеством A) и множество чётных натуральных чисел (которое будем считать множеством B). Оба множества бесконечны, причём A включает B. При этом каждый элемент множества B может быть получен умножением на 2 элемента множества A. Элементы множества B можно пронумеровать, чем устанавливается взаимно однозначное соответствие между множествами A и B.
Об авторе:
Facta loquuntur.
Форма ответа
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Smurf