A COMPARISON OF p-ADIC ANALYSIS AND REAL ANALYIS

The p-adic numbers are an extension of the rational number system which is complete (like the real number system). Some aspects of analysis/calculus work as well in the p-adic field as they do in the real. However, there are many differences between them, both topological and algebraic.

4- Define the field of Q_p of p-adic number

5- prove Hensel’s lemma:

6- Define the derivative .

7- Solve the question as an Example: Show that √(-1) and √4 in field Q5 ?

8- References.

write the math equations, numbers, and the notations in math program to show them in a nice way. For example

Q_p={ 1,2,…}

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