Proof by infinite descent

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Proof by infinite descent

Quality:

The Fermat method - A proof by contradiction used to show that a statement cannot be true for all numbers. If a statement is true for one number, it will also be true for a smaller number, up to infinity, leading to a contradiction and disproving the original statement.. Article "Proof by infinite descent" in English Wikipedia has 30.4 points for quality (as of July 1, 2025). The article contains 18 references and 8 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that language version.

Since the creation of article "Proof by infinite descent", its content was written by 80 registered users of English Wikipedia and edited by 307 registered Wikipedia users in all languages.

The article is cited 41 times in English Wikipedia and cited 221 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #18122 in November 2003
  • Global: #33999 in November 2003

The highest popularity rank from 2008:

  • Local (English): #166695 in August 2011
  • Global: #111528 in August 2011

There are 18 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Proof by infinite descent
30.422
2Galician (gl)
Descenso infinito
20.0587
3Hungarian (hu)
Végtelen leszállás
19.1134
4French (fr)
Méthode de descente infinie
17.3799
5Japanese (ja)
無限降下法
16.5491
6Persian (fa)
نزول نامتناهی
14.6789
7German (de)
Unendlicher Abstieg
14.069
8Spanish (es)
Descenso infinito
12.5163
9Catalan (ca)
Mètode del descens infinit
11.7157
10Chinese (zh)
无穷递降法
8.6333
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Proof by infinite descent" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Proof by infinite descent
412 431
2Japanese (ja)
無限降下法
223 200
3French (fr)
Méthode de descente infinie
70 878
4Russian (ru)
Метод бесконечного спуска
64 611
5Spanish (es)
Descenso infinito
63 214
6Italian (it)
Discesa infinita
40 276
7German (de)
Unendlicher Abstieg
31 228
8Chinese (zh)
无穷递降法
29 823
9Korean (ko)
무한강하법
22 048
10Hebrew (he)
נסיגה אינסופית
10 364
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Proof by infinite descent" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Proof by infinite descent
2 447
2Japanese (ja)
無限降下法
649
3French (fr)
Méthode de descente infinie
339
4Russian (ru)
Метод бесконечного спуска
220
5Chinese (zh)
无穷递降法
159
6German (de)
Unendlicher Abstieg
125
7Italian (it)
Discesa infinita
90
8Spanish (es)
Descenso infinito
82
9Hebrew (he)
נסיגה אינסופית
59
10Korean (ko)
무한강하법
53
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Proof by infinite descent" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Proof by infinite descent
80
2French (fr)
Méthode de descente infinie
50
3German (de)
Unendlicher Abstieg
40
4Italian (it)
Discesa infinita
25
5Japanese (ja)
無限降下法
17
6Spanish (es)
Descenso infinito
15
7Hebrew (he)
נסיגה אינסופית
14
8Chinese (zh)
无穷递降法
13
9Russian (ru)
Метод бесконечного спуска
12
10Hungarian (hu)
Végtelen leszállás
9
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Proof by infinite descent" with the highest AI in June 2025
#LanguageAI awardRelative AI
1Italian (it)
Discesa infinita
1
2Arabic (ar)
نزول غير منته
0
3Catalan (ca)
Mètode del descens infinit
0
4German (de)
Unendlicher Abstieg
0
5English (en)
Proof by infinite descent
0
6Spanish (es)
Descenso infinito
0
7Persian (fa)
نزول نامتناهی
0
8French (fr)
Méthode de descente infinie
0
9Galician (gl)
Descenso infinito
0
10Hebrew (he)
נסיגה אינסופית
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Proof by infinite descent" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Proof by infinite descent
41
2French (fr)
Méthode de descente infinie
39
3Japanese (ja)
無限降下法
18
4German (de)
Unendlicher Abstieg
17
5Hebrew (he)
נסיגה אינסופית
17
6Spanish (es)
Descenso infinito
16
7Hungarian (hu)
Végtelen leszállás
12
8Russian (ru)
Метод бесконечного спуска
10
9Chinese (zh)
无穷递降法
8
10Catalan (ca)
Mètode del descens infinit
7
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
arArabic
نزول غير منته
caCatalan
Mètode del descens infinit
deGerman
Unendlicher Abstieg
enEnglish
Proof by infinite descent
esSpanish
Descenso infinito
faPersian
نزول نامتناهی
frFrench
Méthode de descente infinie
glGalician
Descenso infinito
heHebrew
נסיגה אינסופית
huHungarian
Végtelen leszállás
itItalian
Discesa infinita
jaJapanese
無限降下法
koKorean
무한강하법
nlDutch
Bewijs door oneindige afdaling
ruRussian
Метод бесконечного спуска
slSlovenian
Dokaz z neskončnim spustom
trTurkish
Sonsuz indirgeme teoremi
zhChinese
无穷递降法

Popularity rank trends

Best Rank English:
#166695
08.2011
Global:
#111528
08.2011

AI rank trends

Best Rank English:
#18122
11.2003
Global:
#33999
11.2003

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on The Fermat method from Wikipedia articles about Fermats Last Theorem, Mathematical induction, Proof of Fermats Last Theorem for specific exponents, Proof by contradiction and Vieta jumping. Whereas reading the article about The Fermat method people most often go to Wikipedia articles on Vieta jumping, Well-ordering principle, Diophantine equation, Fermats theorem on sums of two squares and Euclids lemma.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

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About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information