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After the successful spring season IUB offers four new Children's University lectures in October and November, this time twice per date. On Thursday, October 20, Götz Pfander and Michael Stoll, Professors of Mathematics, focused on the mind-boggling problem of numeral infinity. About 250 "children students" between 8-13 years followed the lecture with great interest.
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Oct
21, 2005]
The two lectures, given at 3 p. m. and 5. p. m., started with the two professors quarrelling in a trial of strength: Who knew the largest number? Breathlessly the kids followed the competition. It turned out that no matter how large a number there was always a larger one, always a "plus one"!
The case of Hilbert's Hotel further illustrated numeral infinity: this hypothetical hotel has a room for every number. One day a new guest arrives and is disappointed to learn that, despite the hotel's infinite size, it has no vacancies. Fortunately the clerk has a solution. He simply asks each of the guests to move to the next room. The guest in room 1 moves to room 2, the guest in room 2 to room 3, and so on. This allows the new arrival to slip into the newly vacant room (1) because as there is no end to numbers there is also no end to the hotel rooms and the possibility to house more and more guests. The objection from the audience that there is only a limited number of people on earth was overruled...
The children were introduced to and fascinated by the size of increasingly large numbers like:
Inhabitants of Bremen: 543.000
Inhabitants of Germany: 82.000.000
People of the World: 6.473.829.525
Grains of Sand of the World: 7.500.000.000.000.000.000
Stars in Space: 10.000.000.000.000.000.000.000
The largest known prime number was also presented; it consists of 7.816.230 digits. If printed out 780 sheets of paper are needed - with 10.000 digits printed on each sheet. And this is still a humble number compared to the largest one with a name: one Moser, which is so large that it cannot be presented by “spelling” it out in digits; even mathematicians have hard time imagining it.
Finally the children realized that counting takes a lot of time. If you count for a whole week, a number per second, without eating, drinking or sleeping - you can count until 604.800. In a whole year you could count until 31.536.000 millions. And if you would like to count all the people in the world, that would take up 200 years - which is longer than a lifetime.
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