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== List of numbers appearing in linguistics ==
  
== List of numbers appearing in linguistics ==
−
*There are '''[[26]]''' letters in the Latin alphabet, and 26 in the Greek alphabet.
 +
*There are '''[[26]]''' letters in the Latin alphabet, and 24 in the Greek alphabet.
 
*There are '''676''' two-letter combinations formed from the {{w|ISO basic Latin alphabet}}.
  
*There are '''676''' two-letter combinations formed from the {{w|ISO basic Latin alphabet}}.
−
**It is also the second largest undulating square number; this has been proved by [[David Moews]].
 +
**It is also the second largest [[https://en.wikipedia.org/wiki/Undulating_number|undulating]] square number; this has been proved by [[David Moews]].
 
**676 is an even perfect square number (676 = 26<sup>2</sup>).
  
**676 is an even perfect square number (676 = 26<sup>2</sup>).
 
**Prime factorization of 676 is 2<sup>2</sup> × 13<sup>2</sup>.<ref>https://www.wolframalpha.com/input/?i=676</ref>
  
**Prime factorization of 676 is 2<sup>2</sup> × 13<sup>2</sup>.<ref>https://www.wolframalpha.com/input/?i=676</ref>
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! Language(s)
  
! Language(s)
 
! Analogous number
  
! Analogous number
  +
|-
  +
|Chinese
  +
|8,290,673,451
 
|-
  
|-
 
|Czech
  
|Czech
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|Greek (using Greek alphabet order)
  
|Greek (using Greek alphabet order)
 
|1,967,208,543
  
|1,967,208,543
  +
|-
  +
|Indonesian
  +
|8,246,501,937
 
|-
  
|-
 
|Italian, Portuguese
  
|Italian, Portuguese
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|Latin
  
|Latin
 
|2,908,763,451
  
|2,908,763,451
  +
|-
  +
|Malay
  +
|2,468,519,037
 
|-
  
|-
 
|Polish
  
|Polish
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== Approximations in other notations ==
  
== Approximations in other notations ==
 
For 8,549,176,320:
  
For 8,549,176,320:
−
{| class="article-table"
 +
{| border="0" cellpadding="1" cellspacing="1" class="article-table"
⚫
!Notation
  
−
!Approximation
  
 
|-
  
|-
  ⚫
! scope="col"|Notation
−
|[[BEAF]]
  
  +
! scope="col"|Lower bound
−
|\(\{10,10\}\)
  
  +
! scope="col"|Upper bound
 
|-
  
|-
−
|[[Fast-growing hierarchy]]
 +
|[[Scientific notation]]
  +
|colspan="2" align="center"|\(8.54917632\times10^9\)
⚫
|\(f_2(29)\)
  
  +
|-
  +
|[[Arrow notation]]
  +
|\(45\uparrow6\)
  +
|\(97\uparrow5\)
  +
|-
  +
|[[Steinhaus-Moser Notation]]
  +
|9[3]
  +
|10[3]
  +
|-
  +
|[[Copy notation]]
  +
|7[10]
  +
|8[10]
  +
|-
  +
|[[Chained arrow notation]]
  +
|\(45\rightarrow6\)
  +
|\(97\rightarrow5\)
  +
|-
  +
|[[Taro's multivariable Ackermann function]]
  +
|A(3,29)
  +
|A(3,30)
  +
|-
  +
|[[H* function]]
  +
|H(2)
  +
|H(3)
  +
|-
  +
|[[Pound-Star Notation]]
  +
|#*(1,2,5)*3
  +
|#*(2,2,5)*3
  +
|-
  +
|[[PlantStar's Debut Notation]]
  +
|[5]
  +
|[6]
 
|-
  
|-
 
|[[Hyper-E notation]]
  
|[[Hyper-E notation]]
  +
|85E8
⚫
|\(8E9\)
  
  +
|86E8
 
|-
  
|-
  +
|[[BEAF]] & [[Bird's array notation]]
−
|[[Factorial]]
  
  +
|{45,6}
⚫
|\(14!\)
  
  +
|{97,5}
 
|-
  
|-
−
|[[Scientific notation]]
 +
|[[Bashicu matrix system]]
  +
|(0)[89442]
−
|\(8.549176320 \times 10^9\) (exact)
  
  +
|(0)[89443]
  +
|-
  +
|[[Hyperfactorial array notation]]
  +
|13!
  ⚫
|14!
  +
|-
  +
|[[Fast-growing hierarchy]]
  ⚫
|\(f_2(28)\)
  ⚫
|\(f_2(29)\)
 
|-
  
|-
 
|[[Hardy hierarchy]]
  
|[[Hardy hierarchy]]
  +
|\(H_{\omega^2}(28)\)
 
|\(H_{\omega^2}(29)\)
  
|\(H_{\omega^2}(29)\)
  +
|-
  +
|[[Slow-growing hierarchy]]
  +
|\(g_{\omega^6}(45)\)
  +
|\(g_{\omega^5}(97)\)
 
|}
  
|}
   
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[[Category:Class 1]]
  
[[Category:Class 1]]
 
[[Category:Class 2]]
  
[[Category:Class 2]]
  +
[[Category:Combinatorics]]

Revision as of 15:12, 11 April 2021

This page contains numbers appearing in linguistics (including alphabet-related combinatorics).

List of numbers appearing in linguistics

  • There are 26 letters in the Latin alphabet, and 24 in the Greek alphabet.
  • There are 676 two-letter combinations formed from the ISO basic Latin alphabet.
    • It is also the second largest [[1]] square number; this has been proved by David Moews.
    • 676 is an even perfect square number (676 = 262).
    • Prime factorization of 676 is 22 × 132.[1]
  • There are 702 one- and two-letter combinations formed from the ISO basic Latin alphabet; they are used in chemical element symbols and vehicle registration plates of Germany.
  • There are (including zero) 19 possible onsets, 21 possible nuclei and (including zero) eight possible codas in the spoken Korean language, resulting in 3,192 possible syllables.
  • There are (including zero) 19 possible onsets, 21 possible nuclei and (including zero) 28 possible codas in the written Korean language, resulting in 11,172 possible syllables.
  • In the German language, the number 12,000 is called “zwölftausend”. It is the largest number, whose German name contains different letters.
  • There are 17,576 three-letter combinations formed from the ISO basic Latin alphabet.
  • There are 456,976 four-letter combinations formed from the ISO basic Latin alphabet.
  • 8,549,176,320 not only contains every decimal (base 10) digit (0-9), but all the digits are placed in alphabetical order:
    • 8 = eight, 5 = five, 4 = four, 9 = nine, 1 = one, 7 = seven, 6 = six, 3 = three, 2 = two and 0 = zero.
    • Its prime factorization is: 210 × 33 × 5 × 61,843.
    • The following are numbers that satisfy this property in other languages:
Language(s) Analogous number
Chinese 8,290,673,451
Czech 4,921,085,763
French 5,289,476,310
German 8,315,906,742
Greek (using Greek alphabet order) 1,967,208,543
Indonesian 8,246,501,937
Italian, Portuguese 5,298,467,310
Japanese (Romaji) 5,819,726,340
Klingon (using English transliteration) 2,896,407,513
Latin 2,908,763,451
Malay 2,468,519,037
Polish 4,291,857,630
Russian 8,290,157,346
Spanish 542,986,731 (zero is at the beginning here)
Turkish 6,519,428,037
  • In any top-level domain, there are up to \(36 \times 37^{62}\) possible second-level domain names, but some correspond to illegal contents. This number is equal to 609,269,436,886,430,207,415,724,313,935,118,185,567,366,503,082,897,299,581,429,354,820,868,365,318,591,594,476,323,925,066,482,884.

Approximations in other notations

For 8,549,176,320:

Notation Lower bound Upper bound
Scientific notation \(8.54917632\times10^9\)
Arrow notation \(45\uparrow6\) \(97\uparrow5\)
Steinhaus-Moser Notation 9[3] 10[3]
Copy notation 7[10] 8[10]
Chained arrow notation \(45\rightarrow6\) \(97\rightarrow5\)
Taro's multivariable Ackermann function A(3,29) A(3,30)
H* function H(2) H(3)
Pound-Star Notation #*(1,2,5)*3 #*(2,2,5)*3
PlantStar's Debut Notation [5] [6]
Hyper-E notation 85E8 86E8
BEAF & Bird's array notation {45,6} {97,5}
Bashicu matrix system (0)[89442] (0)[89443]
Hyperfactorial array notation 13! 14!
Fast-growing hierarchy \(f_2(28)\) \(f_2(29)\)
Hardy hierarchy \(H_{\omega^2}(28)\) \(H_{\omega^2}(29)\)
Slow-growing hierarchy \(g_{\omega^6}(45)\) \(g_{\omega^5}(97)\)

Sources

  1. ↑ https://www.wolframalpha.com/input/?i=676
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