Changes: Ducentillion

Revision as of 15:49, 15 December 2020

Not to be confused with duocentillion.

Ducentillion or dihectillion^[1] is equal to 10⁶⁰³ in short scale and 10^1,200 in long scale.^[2] The name is equal with Conway-Wechsler System,^[3] but it seems to be developed independently.

Landon Curt Noll coined the name duocentillion for this number (not to be confused with Bowers' duocentillion, which equals 10³⁰⁹).^[4]^[5]

Aarex Tiaokhiao gave the name bicemillion, referring to the value of this number.^[6]

It is 604 digits long in short scale, or 1,201 digits long in long scale.

Written out in decimal form ducentillion (in the short scale) is:

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
Template:500 zeros

In long scale:

1Template:200 zeros0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}}

Approximations

For short scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{603}\)
Arrow notation	\(10\uparrow603\)
Steinhaus-Moser Notation	251[3]	252[3]
Copy notation	9[603]	10[302]
Chained arrow notation	\(10\rightarrow603\)
H* function	H(200)
Taro's multivariable Ackermann function	A(3,2000)	A(3,2001)
Pound-Star Notation	#((147))15	#((148))15
BEAF & Bird's array notation	{10,603}
Hyper-E notation	E603
Bashicu matrix system	(0)(0)(0)(0)(0)(0)(0)[51396]	(0)(0)(0)(0)(0)(0)(0)[51397]
Hyperfactorial array notation	295!	296!
Fast-growing hierarchy	\(f_2(1992)\)	\(f_2(1993)\)
Hardy hierarchy	\(H_{\omega^2}(1992)\)	\(H_{\omega^2}(1993)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^26+3}}(10)\)

For long scale:

Notation	Lower bound	Upper bound
Scientific notation	\(1\times10^{1200}\)
Arrow notation	\(10\uparrow1200\)
Steinhaus-Moser Notation	451[3]	452[3]
Copy notation	9[1200]	1[1201]
Taro's multivariable Ackermann function	A(3,3983)	A(3,3984)
Pound-Star Notation	#((1182))20	#((1183))20
BEAF	{10,1200}
Hyper-E notation	E1200
Bashicu matrix system	(0)(1)[3]	(0)(1)[4]
Hyperfactorial array notation	524!	525!
Fast-growing hierarchy	\(f_2(3974)\)	\(f_2(3975)\)
Hardy hierarchy	\(H_{\omega^2}(3974)\)	\(H_{\omega^2}(3975)\)
Slow-growing hierarchy	\(g_{\omega^{\omega^3+\omega^22}}(10)\)

Sources

1–9: million · billion · trillion · quadr · quint · sext · sept · oct · non
10–19: decillion · undec · duodec · tredec · quattuordec · quindec · sexdec · septendec · octodec · novemdec
20–29: vigintillion · unvigint · duovigint · tresvigint · quattuorvigint · quinvigint · sesvigint · septemvigint · octovigint · novemvigint
30–39: trigintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
40–49: quadragintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
50–59: quinquagintillion (un- · duo- · tres- · quattuor- · quin- · ses- · septen- · octo- · noven-)
60–69: sexagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
70–79: septuagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septen- · octo- · noven-)
80–89: octogintillion (un- · duo- · tres- · quattuor- · quin- · sex- · septem- · octo- · novem-)
90–99: nonagintillion (un- · duo- · tre- · quattuor- · quin- · se- · septe- · octo- · nove-)
100–900: centillion · ducent · trecent · quadringent · quingent · sescent · septingent · octingent · nongent
1,000–10²⁴: millillion · dumill · dumillinonagintanongent · trimill · trimilliduotrigintatrecent · trimillisexoctogintaoctingent · quadrimill · quadrimilliquattuordecicent · quinmill · sexmill · septimill · octimill · nonimill · myr · decimilliquinsexagintasescent · dumyr · unquadragintamilliunquinquagintacent · centimill · micr · nan · pic · femt · att · zept · yoct

[1] ttps://sites.google.com/site/aarexnumbers/home/ch2/at1i

[2] Illion Numbers

[3] [1]

[4] English names of the first 10000 powers of 10 - American System without dashes

[5] English names of the first 10000 powers of 10 - European System without dashes

[6] Aarex Tiaokhiao's illion numbers^{[dead link]}

[1]

[2]

[3]

[4]

[5]

[6]

@@ Line 1: / Line 1: @@
 {{distinguish|duocentillion}}
-The '''ducentillion''' or '''dihectillion'''<ref>https://sites.google.com/site/aarexnumbers/home/ch2/at1i</ref> is equal to 10<sup>603</sup> in short scale and 10<sup>1,200</sup> in long scale.<ref>[http://www.polytope.net/hedrondude/illion.htm Illion Numbers]</ref> The name is equal with Conway-Wechsler System,<ref>[http://www.mrob.com/pub/math/largenum.html#conway-wechsler]</ref> but it seems to be developed independently.
+'''Ducentillion''' or '''dihectillion'''<ref>https://sites.google.com/site/aarexnumbers/home/ch2/at1i</ref> is equal to 10<sup>603</sup> in short scale and 10<sup>1,200</sup> in long scale.<ref>[http://www.polytope.net/hedrondude/illion.htm Illion Numbers]</ref> The name is equal with Conway-Wechsler System,<ref>[http://www.mrob.com/pub/math/largenum.html#conway-wechsler]</ref> but it seems to be developed independently.
 Landon Curt Noll coined the name '''duocentillion''' for this number (not to be confused with Bowers' [[duocentillion]], which equals 10<sup>309</sup>).<ref>[http://www.isthe.com/chongo/tech/math/number/tenpower.html English names of the first 10000 powers of 10 - American System without dashes]</ref><ref>[http://www.isthe.com/chongo/tech/math/number/tenpowere.html English names of the first 10000 powers of 10 - European System without dashes]</ref>
-[[Aarex Tiaokhiao]] gave the name '''bicemillion''', referring to the value of this number.<ref>[https://sites.google.com/site/aarexnumbers/home/flo2i Aarex Tiaokhiao's illion numbers]</ref>
+[[Aarex Tiaokhiao]] gave the name '''bicemillion''', referring to the value of this number.<ref>[https://sites.google.com/site/aarexnumbers/home/flo2i Aarex Tiaokhiao's illion numbers]{{dead link}}</ref>
+It is 604 digits long in short scale, or 1,201 digits long in long scale.
+Written out in decimal form ducentillion (in the short scale) is:
+{{digits|1000{{100 zeros}}{{500 zeros}}}}
+In long scale:
+{{digits|1{{200 zeros}}{{1000 zeros}}}}
 ==Approximations==
@@ Line 27: / Line 38: @@
 |9[603]
 |10[302]
+|-
+|[[Chained arrow notation]]
+|colspan="2" align="center"|\(10\rightarrow603\)
+|-
+|[[H* function]]
+|colspan="2" align="center"|H(200)
 |-
 |[[Taro's multivariable Ackermann function]]
@@ Line 36: / Line 53: @@
 |#*((148))*15
 |-
-|[[BEAF]]
+|[[BEAF]] & [[Bird's array notation]]
 |colspan="2" align="center"|{10,603}
 |-
@@ Line 43: / Line 60: @@
 |-
 |[[Bashicu matrix system]]
-|(0)(1)[8]
+|(0)(0)(0)(0)(0)(0)(0)[51396]
-|(0)(1)[9]
+|(0)(0)(0)(0)(0)(0)(0)[51397]
 |-
 |[[Hyperfactorial array notation]]
@@ Line 97: / Line 114: @@
 |-
 |[[Bashicu matrix system]]
-|(0)(1)[9]
+|(0)(1)[3]
-|(0)(1)[10]
+|(0)(1)[4]
 |-
 |[[Hyperfactorial array notation]]
@@ Line 121: / Line 138: @@
 == See also ==
 {{illion}}
+[[Category: Tier 1 -illion numbers]]
 [[Category:Numbers]]
 [[Category:Illion]]