Mathematical lawlessness. From elementary mathematics to sublime abstraction n (Beyond Infinity: An expedition to the outer limits of the mathematical universe)

I read this book by Eugenia Cheng four years ago and it seemed interesting to me because the author literally talks about the concept of infinity on her fingers, and she does it charmingly and with good humor:) As a literal first example, the endless Hilbert hotel and the occupancy of another tenant in a full hotel are analyzed. Then there are two, three and infinity hotels, which must be evicted in a one-storey Hilbert bungalow:) Eugenia leads us to the mathematical concept of infinity. In this way, natural, integer, rational and irrational numbers are exploited. But it turns out to fully define the concept of infinity after the transition to set theory, and then it turns out to determine infinities of different sizes:) It is interesting to understand the difference between cardinal and ordinal numbers. But the infinitely small numbers seemed boring, because they set out the basic things from calculus, which at one time were told in high school and in more detail at the first courses of technical universities.

In general, the book turned out to be interesting, with a good presentation and written in very clear language, which is not so common for books on mathematics:)

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