Why is adic number P?
Why is adic number P?
The p-adic absolute value gives us a new way to measure the distance between two numbers. The p-adic distance between two numbers x and y is the p-adic absolute value of the number x-y. So going back to the 3-adics, that means numbers are closer to each other if they differ by a large power of 3.
What is p-adic expansion?
In mathematics, the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.
What is the p-adic metric?
A -adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime are related to proximity in the so called ” -adic metric.”
What is P in number theory?
In set theory, P(X) means the power set of X. In geometry, P can refer to a projective space although it is also often the name given to a particular point. 8.4K views.
Are P-ADIC numbers ordered?
Here’s a final curious fact about the p-adic numbers. We all know that if x and y are two non-equal real numbers then either xthere is no linear ordering of the p-adic numbers!
Is the P-ADIC integers complete?
The p-adic integers can also be seen as the completion of the integers with respect to a p-adic metric. Let us introduce a p-adic valuation on the integers, which we will extend to Zp.
How do you calculate P-ADIC expansion?
The proof of Theorem 3.1 gives an algorithm to compute the p-adic expansion of any rational number in Zp: (1) Assume r < 0. (If r > 0, apply the rest of the algorithm to −r and then negate with (2.2) to get the expansion for r.) (2) If r ∈ Z<0 then write r = −R and pick j ≥ 1 such that R < pj.
What is the meaning of ADIC?
ADIC
| Acronym | Definition |
|---|---|
| ADIC | Advertising and Integrated Communications (course) |
| ADIC | Aerospace Defense Intelligence Center |
| ADIC | Air Defense Intelligence Center |
| ADIC | AFSCF Development Integration Committee |
Who invented P-ADIC numbers?
mathematician Kurt Hensel
The p-adic numbers were invented at the beginning of the twentieth century by the German mathematician Kurt Hensel (1861–1941). The aim was to make the methods of power series expansions, which play such a dominant role in the theory of functions, available to the theory of numbers as well.
What are the applications of p-adic analysis?
Applications of p -adic analysis have mainly been in number theory, where it has a significant role in diophantine geometry and diophantine approximation. Some applications have required the development of p -adic functional analysis and spectral theory.
What is p-adic quantum mechanics?
P-adic quantum mechanics is a relatively recent approach to understanding the nature of fundamental physics. It is the application of p-adic analysis to quantum mechanics. The p-adic numbers are a counterintuitive arithmetic system that was discovered by the German mathematician Kurt Hensel in about 1899.
What are p-adic numbers?
The p-adic numbers are an intuitive arithmetic system (but geometrically counterintuitive) that was discovered by German mathematician Kurt Hensel in about 1899 and by German mathematician Ernst Kummer (1810-1893) earlier in elementary form. The closely related adeles and ideles were introduced in the 1930s by Claude Chevalley and André Weil.
What is padic analysis in math?
p-adic analysis. In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers.
