Curious p-adic numbers
At the turn of the 20th century, the algebraist Kurt Hensel had the genius intuition that led to the invention of p-adic numbers. The resulting system is baffling: no need for a minus sign, the need to develop a new form of proximity between numbers, the appearance of an astonishing topology, and above all… deep applications in all areas of mathematics! The very writing of these numbers, which differs depending on the approaches (they can even be written with "decimals to the left"), is surprising. Thus, a negative number like –1 is represented using an infinite sequence of digits or as the sum of a series one might think diverges. A true poetry of numbers!
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A dive into a strange world of numbers
At the beginning of the 20th century, the German mathematician Kurt Hensel "invented" new numbers, written with infinitely many digits as in the decimal system, but based on a very different notion of proximity. This curious theory has proved highly fruitful in arithmetic!
Dyadic tree: integers and p-adic order | Tangente
Starting from a tree whose leaves extend indefinitely, we can construct either the positive integers or the dyadic integers. The trick? Put the 0s and 1s in the right places.
Kurt Hensel, father of p-adic numbers | Tangente
Kurt Hensel is best known for his work on p-adic numbers.