• Aucun résultat trouvé

# How to prove that a number is irrational?

N/A
N/A
Protected

Academic year: 2022

Partager "How to prove that a number is irrational?"

Copied!
14
0
0
En savoir plus ( Page)

Texte intégral

(1)

k1

k2

h

h

k−k1

k−k2

k

h

1

(2)

j

j0

(3)

j0

N−1

j0

(4)

n

n

x1

xn

n

n

n

α

n

n≥0

n

n−1

n−2

n→∞

n−1

n

n−1

−1

−1

(5)

−1

−1

n

n≥0

n

n−1

n−2

n

n≥0

−1

n

n≥0

n

n

n

−n

n

n

n

n≥2

n

n

n−1

n→∞

n

n

n

n−1

n−1

n−1

n−1

n

n

−1

n−1

n

−1

n

−1

n

n

n−1

n

n−1

n

n−2

n−3

(6)

0

0

0

0

0

0

0

2

(7)

| |

| |

| | | |

|

|

|

|

m

m

m

m

m

q∈Z, q→∞

m

m

m∈Z

m

m

m

m

m

m

m

(8)

−1

−1

−1

N

n=0

n

k≥1

N+k

0

d

(9)

d

d

d

d

d

i=1

i

0

d

i=2

i

i

i

d

d

i=2

i

d

0

a

n≥0

−n!

d

(10)

|t−α|≤1

0

d

i=2

j

d

d

## 3 Third course: December 8, 2018.

κ

κ

N

N

n=0

N!−n!

a

k≥1

(11)

a

N

3

3

3

3

3

3

3

η

(12)

3

3

η

>0

κ

(13)

n=0

−dλκne

3

d

3

d

κ

d−κ

(14)

−2−

### https://webusers.imj-prg.fr/~michel.waldschmidt/articles/pdf/IntroductionDiophantineMethods.pdf

Références

Documents relatifs

La présente étude a mise en évidence une diminution du cumul de précipitations annuelles, du nombre de jours pluvieux, du nombre de jours de pluies intenses et du nombre de jours

Infection with the protozoan Toxoplasma gondii is one of the most frequent parasitic infections worldwide. This obligate intracellular parasite was first described

Theorem 2 The expected size of the visibility complex of n uniformly distributed unit balls..

Suppose R is a right noetherian, left P-injective, and left min-CS ring such that every nonzero complement left ideal is not small (or not singular).. Then R

Prove that the gamma distribution is actually a continuous probability distributions that is it is non-negative over x &gt; 0 and its integral over R + is equal to 1.. Exercise 8

La CPU souhaite l’augmentation du préciput de l’Agence Nationale de la Recherche (ANR) et demande que cette augmentation soit attribuée aux universités sans aucun

L’aspiration sociale de ce PTCE s’objective dans son nom : TETRIS pour Transition Ecologique Territoriale par la Recherche et l’Innovation Sociale qui définit

A finished VAXELN system runs directly on a &#34;target&#34; processor without the presence of an operating system~ Typical VAXELN applications are dedicated,

Dans la première partie, nous avons étudié le comportement magnétique de la machine synchrone a aimants permanents en régime sain et en défaut de court-circuit

Given a Hilbert space H characterise those pairs of bounded normal operators A and B on H such the operator AB is normal as well.. If H is finite dimensional this problem was solved

It is intended to be the firmware reference manuaL and to be used by the advanced microprogrammer of the Rikke MathiLda system.. WideStore, WS, is the common

The forwat in this section uses a machine line heading with a listing of manuals for each operating system version and the appropriate product set members

We define a partition of the set of integers k in the range [1, m−1] prime to m into two or three subsets, where one subset consists of those integers k which are &lt; m/2,

It is expected that the result is not true with = 0 as soon as the degree of α is ≥ 3, which means that it is expected no real algebraic number of degree at least 3 is

UNIVERSITY OF NATURAL SCIENCES HO CHI MINH City http://www.hcmuns.edu.vn/?. Introduction to

It is expected that the result is not true with &#34; = 0 as soon as the degree of α is ≥ 3, which means that it is expected no real algebraic number of degree at least 3 is

It is expected that the result is not true with = 0 as soon as the degree of α is ≥ 3, which means that it is expected no real algebraic number of degree at least 3 is

Given a pencil of algebraic plane curves such that a general element is irreducible, the purpose of this paper is to give a sharp upper bound for the number of reducible curves in

It should not be possible to bypass authentication or encryption by asking for a different address for the same host.. Source Routing and

While the IPv6 protocols are well-known for years, not every host uses IPv6 (at least in March 2009), and most network users are not aware of what IPv6 is or are even afraid

During the survey, I noted anomalies in a few dozen hosts’ SMTP servers; examples included a RSET command causing the server to close the connection, a VRFY POSTMASTER evoking a

Recent developments in p-adic logic [4] have raised the question of whether there exists an anti-almost closed, discretely A-onto and smoothly lo- cal compactly singular, stable

Moreover, if Θ is minimal, generic, totally bijective and complete then Fermat’s conjecture is false in the context of multiplicative, algebraically Euclidean, linear primes.. Let

Sélectionne ta langue

Le site sera traduit dans la langue de ton choix.

Langues suggérées pour toi :

Autres langues