R daje sie latwo przeksztalcic w dowolny odcinek otwarty, np. Stad juz latwo dowiesc rownolicznosci zbioru P N i odcinka [0,1 pewnie dla jeszcze wiekszego skrocenia mozna sie posluzyc twierdzeniem Cantora-Bernsteina.Ĭantora-Bernsteina daje odpowiedz natychmiast. Ale kazdy ciag zer i jedynek odpawiada funkcji charakterystycznej jakiegos podzbioru zbioru N i to wzajemnie jednoznacznie. You can add this document to your study collection s Sign in Available only to authorized users.ĭescription optional.Lepsze prostsze? Kazda liczba z odcinka [0,1 ma rozwiniecie dwojkowe 0,abcd A zatem kazda liczba moze byc przeksztalcona na ciag zer i jedynek. Zbiory o mocy continuum, porównywanie mocy Wszystkie liczby rzeczywistych oznaczamy symbolem. Tymczasem w logice matematycznej takie zdanie jest prawdziwe! Zbiory oznaczamy wielkimi literami, np. Flashcards Collections.ĭocuments Last activity. If one of us were in hospital, others would probably find a way to bring him there anyway,” he says jokingly.For complaints, use another form.
“We want to keep this tradition for the rest of our lives, no matter what.
“I remember one time my flight was cancelled and I drove all night to get to Copco Lake on time and pose for the photo,” Brian recalls. They’ve even agreed to collect money if one of them isn’t able to afford the trip. They do everything to meet every five years. Since the first photo together, the men have gone their own ways, but they all agree that those trips to the lake have been the glue that keeps them together. “But we all decided this time it was better to take the photo with our T-shirts on.” “We haven’t changed much since we were teenagers,” John laughs. David is holding a pet cockroach in a different jar, though. The day is cloudy just like in 1982, when the first photo was taken. In the latest picture they took they are sitting in identical positions with unchanged, mysterious expressions on their faces. The others liked his idea and in this way a tradition was born. And then Mark said it would be fun to do it every five years. One day when Brian set his camera to take a group photo, John suggested they could recreate the 1982 pose in the photo and together with Dallas worked on the details. David is pictured holding a coffee jar with a cockroach inside, which the guys kept as a pet. It showed five teens, three of them without their T-shirts on, with hairdos typical of the time. Brian grabbed John’s camera, gathered all his friends and set the self-timer to take a group photo. “We finished high school and it was our last summer before going to college so we wanted to relax, have fun and forget about the responsibilities we were expected to take on.” The first photograph of the high school friends was just accidental. “I wanted to share this place with my friends so I invited Brian, Mark, Dallas and David to join me there,” says John. John used to go fishing there with his grandfather. They had built a hut on the lake in the mid-seventies. When five teenagers sat down and posed for a picture at Copco Lake in 1982, they didn’t plan to make it a tradition.
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