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Although infinity lurks in mathematics at every turn, it is only relatively recently that we have learned to study it. Or rather, not so much "it" as "it", because as mathematicians have discovered with astonishment, there is in fact not one infinity, but infinitely many. They create various systems of "transfinite numbers", which extend the good old natural numbers. During the lecture by Dr. Tomasz Miller, we will look at some of such systems, including the so-called cardinal numbers and ordinal numbers, as well as Conway's superreal numbers, which, in addition to infinitely large objects, also contain infinitely small objects. Of course, there will be no shortage of attempts to answer the question: "What is all this for?" Closer to Science is a series of popular science lectures organized at the Faculty of Physics, Astronomy and Applied Computer Science of the Jagiellonian University in Krakow. https://blizejnauki.fais.uj.edu.pl/