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FORMAL NUMBERS

"God created the integers, all else is the work of man..."

Leopold Kronecker


We first recall the basic facts about the different families of numbers which are at the beginning of all mathematical constructions in number theory. Different extensions of the notion of number exist. An old one is the notion of complex number which is widely known and very useful for physical sciences. Another and more recent one is the notion of p-adic number based upon a prime number p. Here we are considering a different kind of numbers which are also, but in a different way, closely related to prime numbers.

 

1) From natural integers to real numbers   p. 2-3

2) Fields of power series   p. 4-7

3) Formal numbers over a finite field   p. 8-10

 

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