First Encounter with Infinity
In the first lecture we discuss the dangers that are inherently present when we transcend our finite intuition and consider infinite quantities, constructions etc.
The first step to do is to clean up our language, restricting it to the most transparent and unambiguous grammar and vocabulary. This is the language of the sets and operations on them, and logical formulas involving quantifiers, to formulate meaningful (true or false) constructions.
Read the first lecture here.
P.S. Yet another funny and instructive book by N. Ya. Vilenkin, “In Search of Infinity”, can be downloaded here. Read slowly and enjoy!