The report by Yuri Lisitsa is dedicated to Conway numbers, ordinals, and paradoxes of set theory. In Yuri Lisitsa's report, strict mathematics intersects with philosophical imagination, and abstract constructions become a way to look at infinity, motion, and limits differently. The talk will cover the form of Conway numbers and the properties of ordinal numbers related to the "jumps" of infinite sequences and symmetric "compressions" of their inverse values. The lecture will be interesting for those who enjoy complex intellectual journeys and are not afraid of rich theory. This event is for students, researchers, teachers, and listeners of philosophical and mathematical cycles. The speaker will offer not a retelling of known truths, but an attempt to view fundamental paradoxes differently. Entertainment in Moscow is collected on our website.