Точная верхняя и нижняя границы

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Точная верхняя и нижняя границы

Quality:

Infimum and supremum - least (resp. greatest) of majoring (resp. minoring) elements of a partially ordered set (not necessarily existing in all sets). Article “Точная верхняя и нижняя границы” in Russian Wikipedia has 12.9 points for quality (as of July 1, 2025). The article contains 0 references and 11 sections. The article also contains templates indicating quality issues, therefore its score was reduced by 0.68 points.

This article has the best quality in English Wikipedia. Also, this article is the most popular in that (Russian) language version.

Since the creation of article “Точная верхняя и нижняя границы”, its content was written by 62 registered users of Russian Wikipedia and edited by 654 registered Wikipedia users in all languages.

The article is cited 146 times in Russian Wikipedia and cited 2197 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (Russian): #95 in December 2005
  • Global: #209 in March 2002

The highest popularity rank from 2008:

  • Local (Russian): #11698 in January 2015
  • Global: #28869 in October 2019

There are 19 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)
Infimum and supremum
43.5146
2Indonesian (id)
Infimum dan supremum
38.6615
3German (de)
Infimum und Supremum
27.6011
4Galician (gl)
Ínfimo e supremo
26.523
5Simple English (simple)
Infimum and supremum
25.0848
6Croatian (hr)
Supremum i infimum
22.1266
7Polish (pl)
Kresy dolny i górny
21.904
8Persian (fa)
اینفیمم و سوپریمم
21.3494
9French (fr)
Borne supérieure et borne inférieure
13.8169
10Portuguese (pt)
Supremo e ínfimo
13.468
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 "Точная верхняя и нижняя границы" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Infimum and supremum
3 796 229
2German (de)
Infimum und Supremum
1 052 103
3Russian (ru)
Точная верхняя и нижняя границы
756 752
4French (fr)
Borne supérieure et borne inférieure
569 391
5Spanish (es)
Elemento supremo e ínfimo
415 184
6Polish (pl)
Kresy dolny i górny
382 916
7Italian (it)
Estremo superiore e estremo inferiore
344 092
8Portuguese (pt)
Supremo e ínfimo
182 692
9Korean (ko)
상한과 하한
121 689
10Persian (fa)
اینفیمم و سوپریمم
66 015
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 "Точная верхняя и нижняя границы" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Infimum and supremum
10 412
2Russian (ru)
Точная верхняя и нижняя границы
2 019
3German (de)
Infimum und Supremum
1 711
4French (fr)
Borne supérieure et borne inférieure
1 117
5Polish (pl)
Kresy dolny i górny
560
6Spanish (es)
Elemento supremo e ínfimo
513
7Korean (ko)
상한과 하한
429
8Italian (it)
Estremo superiore e estremo inferiore
320
9Portuguese (pt)
Supremo e ínfimo
274
10Hebrew (he)
אינפימום וסופרמום
212
More...

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

The highest AI

Language versions of the article "Точная верхняя и нижняя границы" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Infimum and supremum
204
2German (de)
Infimum und Supremum
114
3French (fr)
Borne supérieure et borne inférieure
76
4Russian (ru)
Точная верхняя и нижняя границы
62
5Italian (it)
Estremo superiore e estremo inferiore
47
6Spanish (es)
Elemento supremo e ínfimo
38
7Polish (pl)
Kresy dolny i górny
37
8Korean (ko)
상한과 하한
14
9Persian (fa)
اینفیمم و سوپریمم
13
10Hebrew (he)
אינפימום וסופרמום
13
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 "Точная верхняя и нижняя границы" with the highest AI in June 2025
#LanguageAI awardRelative AI
1Ukrainian (uk)
Інфімум та супремум
1
2Catalan (ca)
Suprem i ínfim (elements)
0
3German (de)
Infimum und Supremum
0
4English (en)
Infimum and supremum
0
5Spanish (es)
Elemento supremo e ínfimo
0
6Basque (eu)
Beheren eta goren
0
7Persian (fa)
اینفیمم و سوپریمم
0
8French (fr)
Borne supérieure et borne inférieure
0
9Galician (gl)
Ínfimo e supremo
0
10Hebrew (he)
אינפימום וסופרמום
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 "Точная верхняя и нижняя границы" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Infimum and supremum
589
2French (fr)
Borne supérieure et borne inférieure
286
3Korean (ko)
상한과 하한
220
4German (de)
Infimum und Supremum
206
5Russian (ru)
Точная верхняя и нижняя границы
146
6Polish (pl)
Kresy dolny i górny
135
7Spanish (es)
Elemento supremo e ínfimo
132
8Italian (it)
Estremo superiore e estremo inferiore
99
9Portuguese (pt)
Supremo e ínfimo
72
10Ukrainian (uk)
Інфімум та супремум
65
More...

Scores

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

Quality measures

Interwikis

#LanguageValue
caCatalan
Suprem i ínfim (elements)
deGerman
Infimum und Supremum
enEnglish
Infimum and supremum
esSpanish
Elemento supremo e ínfimo
euBasque
Beheren eta goren
faPersian
اینفیمم و سوپریمم
frFrench
Borne supérieure et borne inférieure
glGalician
Ínfimo e supremo
heHebrew
אינפימום וסופרמום
hrCroatian
Supremum i infimum
idIndonesian
Infimum dan supremum
itItalian
Estremo superiore e estremo inferiore
koKorean
상한과 하한
plPolish
Kresy dolny i górny
ptPortuguese
Supremo e ínfimo
ruRussian
Точная верхняя и нижняя границы
simpleSimple English
Infimum and supremum
srSerbian
Инфимум и супремум
ukUkrainian
Інфімум та супремум

Popularity rank trends

Best Rank Russian:
#11698
01.2015
Global:
#28869
10.2019

AI rank trends

Best Rank Russian:
#95
12.2005
Global:
#209
03.2002

Local AI rank history

Global AI rank history

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Infimum and supremum from Wikipedia articles about Limit inferior and limit superior, Kolmogorov–Smirnov test, Lattice, Logistic function and Lebesgue measure. Whereas reading the article about Infimum and supremum people most often go to Wikipedia articles on Partially ordered set, Upper and lower bounds, Greatest and least elements, Least-upper-bound property and Limit inferior and limit superior.

Cumulative results of quality and popularity of the Wikipedia article

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

News from 13 October 2025

On 13 October 2025 in multilingual Wikipedia, Internet users most often read articles on the following topics: Diane Keaton, Ed Gein, 2026 FIFA World Cup qualification, 2026 FIFA World Cup, 2026 FIFA World Cup qualification (UEFA), Ian Watkins, 2026 FIFA World Cup qualification (CAF), Ilse Koch, Donald Trump, ChatGPT.

In Russian Wikipedia the most popular articles on that day were: Яндекс, Томагавк (ракета), Гин, Эд, Китон, Дайан, IMGSRC.RU, Покров Пресвятой Богородицы, Список умерших в 2025 году, Чемпионат мира по футболу 2026, ЯRUS, Война в Газе.

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