Několik poznámek k mohutnosti množin
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The Union of czech mathematicians and physicists
Abstract
Text je stručným přehledem nejdůležitějších vlastností nekonečných množin, mimo jiné vyvrací omyl publikovaný v článku Kuřina & Vondrová: Nekonečno, jak to vlastně je, UM 2003. "Zip Petera Zamarovského" není bijekcí mezi (0;1)x(0;1) a (0;1), ale pouze injekcí, tudíž ekvivalenci množiny všech bodů čtverce a úsečky nedokazuje. V článku je naznačen jiný důkaz.
This paper deals with some problems of the sets cardinality. It explains the concept of countability and uncountability. It discovers the incorrectness of the previously described construction of the bijection betwen the square and its side. It provides a correct proof of the existence of this mapping and describes the construction of higher cardinalities with a technique that is understandable for talented secondary school students.
This paper deals with some problems of the sets cardinality. It explains the concept of countability and uncountability. It discovers the incorrectness of the previously described construction of the bijection betwen the square and its side. It provides a correct proof of the existence of this mapping and describes the construction of higher cardinalities with a technique that is understandable for talented secondary school students.
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Subject(s)
Konečná množina, Nekonečná množina, Bijekce, Ekvivalence množin, Kardinální číslo
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ISSN
1210-9037