Tomás and Amoretti: Generating Function and Generating Number for the Natural Series

The natural series is a sequence of all natural numbers arranged in ascending order. The study of mathematics begins with the natural series. It's simple. Interest in mathematics appears when we accidentally learn that the natural series is a complex mathematical object. We learn that a function or a number can generate the natural series. The natural numbers that form it do not necessarily have to increase; another order is possible, which has both mathematical and physical, deep meaning. We also learn that a series equal to the sum of all natural numbers decomposes into a product of two infinite series. And so on. The Portuguese mathematician Álvaro Tomás (16th c.) and the French mathematician E.-M. Amoretti (19th c.) were among the first to say something new about the natural series.
The lecture duration is 90 minutes.
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