2835: Factorial Numbers - Revision history

172.70.91.245: Edited the well-meant addition to be more correct than its original statement. If still suitable to be said (but didn't want to delete it, with the OP not knowing where their limit was wrong and maybe would try again).

2025-04-07T15:29:46Z

Edited the well-meant addition to be more correct than its original statement. If still suitable to be said (but didn't want to delete it, with the OP not knowing where their limit was wrong and maybe would try again).

162.158.216.159: /* Explanation */

2025-04-07T13:48:31Z

‎Explanation

172.69.208.188: Corrected the base numbers in the transcript.

2025-04-05T01:38:19Z

Corrected the base numbers in the transcript.

172.71.124.39: /* Transcript */

2024-12-22T16:42:02Z

‎Transcript

FaviFake: removed Category:Popular Comics using HotCat

2024-11-02T10:53:41Z

removed Category:Popular Comics using HotCat

172.69.79.191: Thanks for reminding me that this needed retabling. I think this works, but I'm not sure if there'd be concensus about it... Letting others mull over it.

2024-10-11T22:42:05Z

Thanks for reminding me that this needed retabling. I think this works, but I'm not sure if there'd be concensus about it... Letting others mull over it.

Xurkitree10: /* Transcript */

2024-10-11T09:01:53Z

‎Transcript

172.69.194.204 at 19:02, 15 March 2024

2024-03-15T19:02:43Z

172.70.91.62 at 18:06, 15 March 2024

2024-03-15T18:06:51Z

172.70.91.61 at 18:06, 15 March 2024

2024-03-15T18:06:21Z

@@ Line 16: / Line 16: @@
 In the comic, [[Cueball]] proposes a {{w|factorial number system}}, where the base ''changes'' for each place value - the first digit can be 0 or 1, the next digit can be 0, 1, or 2, the third can be 0, 1, 2, or 3, and so on.  Each place value is the factorial of the base.  So the number 137 in base 10 could be written as 10221, meaning 1×5! + 0×4! + 2×3! + 2×2! + 1×1!.  While this numbering system is technically usable and can express any number, it seems excessively complicated, and the only reason Cueball gives for using it is that he thinks large digits like 9 should only be used in vast numbers (9 would not be used unless the number was at least 9 digits long, or over 3.2 million in decimal).  This is a silly reason for using a new numbering system,{{cn}} so the math department thinks this is a prank, and has security throw him out.
-In the title text, someone points out that a factorial number system needs more and more digits for each place value.  The tenth digit in a factorial number would be in base 11, which needs 11 possible digits, and 0-9 only provides 10.  In bases higher than 10, you can use letters to represent higher digits.  For example, hexadecimal (base 16) goes from 0 to 9, then from A to F.  It would be reasonable to do the same thing for higher bases in factorial numbers.  Instead, Cueball says that it's simply illegal to write numbers larger than about 3.6 million, the largest you can go without using a base greater than 10. This is an absurd limitation, as other numbering systems can go as high as you like. (Except Roman numerals, that can only go to MMMCMXCIX.)
+In the title text, someone points out that a factorial number system needs more and more digits for each place value.  The tenth digit in a factorial number would be in base 11, which needs 11 possible digits, and 0-9 only provides 10.  In bases higher than 10, you can use letters to represent higher digits.  For example, hexadecimal (base 16) goes from 0 to 9, then from A to F.  It would be reasonable to do the same thing for higher bases in factorial numbers.  Instead, Cueball says that it's simply illegal to write numbers larger than about 3.6 million, the largest you can go without using a base greater than 10. This is an absurd limitation, as other positional numbering systems can go as high as you like, and possibly have room for. (Roman numerals, that use a non-positional system, are said to only go to MMMCMXCIX, or 3999 in decimal, but {{w|Roman numerals#Large numbers|there are already various ways}} to exceed this. Practically, the upper limit is still only that of space to write them and any inconvenience in doing so.)
 The number at the top of Cueball's presentation, 353011, is 3×6! + 5×5! + 3×4! + 0×3! + 1×2! + 1×1! which gives the decimal value of 2835, the number of the comic.

@@ Line 16: / Line 16: @@
 In the comic, [[Cueball]] proposes a {{w|factorial number system}}, where the base ''changes'' for each place value - the first digit can be 0 or 1, the next digit can be 0, 1, or 2, the third can be 0, 1, 2, or 3, and so on.  Each place value is the factorial of the base.  So the number 137 in base 10 could be written as 10221, meaning 1×5! + 0×4! + 2×3! + 2×2! + 1×1!.  While this numbering system is technically usable and can express any number, it seems excessively complicated, and the only reason Cueball gives for using it is that he thinks large digits like 9 should only be used in vast numbers (9 would not be used unless the number was at least 9 digits long, or over 3.2 million in decimal).  This is a silly reason for using a new numbering system,{{cn}} so the math department thinks this is a prank, and has security throw him out.
-In the title text, someone points out that a factorial number system needs more and more digits for each place value.  The tenth digit in a factorial number would be in base 11, which needs 11 possible digits, and 0-9 only provides 10.  In bases higher than 10, you can use letters to represent higher digits.  For example, hexadecimal (base 16) goes from 0 to 9, then from A to F.  It would be reasonable to do the same thing for higher bases in factorial numbers.  Instead, Cueball says that it's simply illegal to write numbers larger than about 3.6 million, the largest you can go without using a base greater than 10. This is an absurd limitation, as other numbering systems can go as high as you like.
+In the title text, someone points out that a factorial number system needs more and more digits for each place value.  The tenth digit in a factorial number would be in base 11, which needs 11 possible digits, and 0-9 only provides 10.  In bases higher than 10, you can use letters to represent higher digits.  For example, hexadecimal (base 16) goes from 0 to 9, then from A to F.  It would be reasonable to do the same thing for higher bases in factorial numbers.  Instead, Cueball says that it's simply illegal to write numbers larger than about 3.6 million, the largest you can go without using a base greater than 10. This is an absurd limitation, as other numbering systems can go as high as you like. (Except Roman numerals, that can only go to MMMCMXCIX.)
 The number at the top of Cueball's presentation, 353011, is 3×6! + 5×5! + 3×4! + 0×3! + 1×2! + 1×1! which gives the decimal value of 2835, the number of the comic.

@@ Line 23: / Line 23: @@
 ==Transcript==
-{{incomplete transcript|Do NOT delete this tag too soon. - De-tabled the Transcript (thanks for reminding me), but definitely still needs work...}}
 :[Cueball is standing in front of a large presentation poster. There are two uniformed officers (a Ponytail and a further Cueball, wearing badged hats) approaching Cueball.]
 :[Poster:]
@@ Line 33: / Line 33: @@
 :::[Rightmost stack:] Base 2 [square:] 1
 :::[2nd rightmost stack:] Base 3 [square:] 1
-:::[3rd rightmost stack:] Base 4 [square:] 1
+:::[3rd rightmost stack:] Base 4 [square:] 0
-:::[4th rightmost stack:] Base 5 [square:] 0
+:::[4th rightmost stack:] Base 5 [square:] 3
 :::[5th rightmost stack:] Base 6 [square:] 5
 :::[6th rightmost stack:] Base 7 [square:] 3

@@ Line 37: / Line 37: @@
 :::[5th rightmost stack:] Base 6 [square:] 5
 :::[6th rightmost stack:] Base 7 [square:] 3
-:::[Leftmost stack has no obvious text, its square is cut across by the 'torn' edge of the diagram.]
+:::[Leftmost stack is cut across by the 'torn' edge of the diagram. Square seemingly contains a 0.]
 ::[Two column-pairs, with idential paired-headers, above (generally) a 'number', a linking dash and another 'number']

← Older revision		Revision as of 10:53, 2 November 2024
Line 81:		Line 81:
	[[Category:Comics featuring Ponytail]] <!-- Hatted 'security officer' -->		[[Category:Comics featuring Ponytail]] <!-- Hatted 'security officer' -->
	[[Category:Multiple Cueballs]] <!-- If including otherwise cueball-like hatted 'security officer' of no other distinction -->		[[Category:Multiple Cueballs]] <!-- If including otherwise cueball-like hatted 'security officer' of no other distinction -->
−	~~[[Category:Popular Comics]]~~

@@ Line 23: / Line 23: @@
 ==Transcript==
-:[Cueball is standing in front of a large poster. There are two uniformed officers (a Ponytail and a further Cueball, wearing badged hats) approaching Cueball.]
+{{incomplete transcript|Do NOT delete this tag too soon. - De-tabled the Transcript (thanks for reminding me), but definitely still needs work...}}
 :[Poster:]
-: Variable-base Factoradic™ numbers
+::[Title:]Variable-base Factoradic™ numbers
-: Left side
+::[Diagram in the form of a slip of paper, left edge torn jagged to indicate indefinite continuation]
-:{| class="wikitable"
+::[Two column-pairs, with idential paired-headers, above (generally) a 'number', a linking dash and another 'number']
-|Base 10||Factoradic
+:::[Left headers for both:] Base 10
-|-
+:::[Right headers for both:] Factoradic
-|1||1
+:::[First column of number pairs:]
-|-
+::::1 &mdash; 1
-|2||10
+::::2 &mdash; 10
-|-
+::::3 &mdash; 11
-|3||11
+::::4 &mdash; 20
-|-
+::::5 &mdash; 21
-|4||20
+::::6 &mdash; 100
-|-
+::::7 &mdash; 101
-|5||21
+::::[Gap]
-|-
+::::21 &mdash; 311
-|6||100
+::::22 &mdash; 320
-|-
+::::23 &mdash; 321
-|7||101
+:::[Continuation in second column of number pairs:]
-|-
+::::24 &mdash; 1,000
+::::25 &mdash; 1,001
-|-
+::::[Gap]
-|21||311
+::::5,038 &mdash; 654,320
-|-
+::::5,039 &mdash; 654,321
-|22||320
+::::5,040 &mdash; 1,000,000
-|-
+::::[Gap]
-|23||321
+::::999,998 &mdash; 266,251,210
-|}
+::::999,999 &mdash; 266,251,211
+::::1,000,000 &mdash; 266,251,220
-: Right side
+::::1,000,001 &mdash; 266,251,221
 :Cueball: Small numbers like seven or nineteen shouldn't use big numerals like "7" or "9".

← Older revision		Revision as of 19:02, 15 March 2024
Line 10:		Line 10:

	==Explanation==		==Explanation==
−	~~{{incomplete\|Revised but needs review from an actual mathematician. Also, are there any practical uses for factorial numbers? Do NOT delete this tag too soon.}}~~
−	~~--> There aren't any practical uses for it, mostly because it uses 9 bases, which would take many years of numerical base training.~~
−
	A {{w\|factorial}} is a product of positive integers. For instance, four factorial, written '4!', means 4×3×2×1=24.		A {{w\|factorial}} is a product of positive integers. For instance, four factorial, written '4!', means 4×3×2×1=24.

@@ Line 11: / Line 11: @@
 ==Explanation==
 {{incomplete|Revised but needs review from an actual mathematician.  Also, are there any practical uses for factorial numbers?  Do NOT delete this tag too soon.}}
+--> There aren't any practical uses for it, mostly because it uses 9 bases, which would take many years of numerical base training.
 A {{w|factorial}} is a product of positive integers. For instance, four factorial, written '4!', means 4×3×2×1=24.

@@ Line 5: / Line 5: @@
 | image     = factorial_numbers_2x.png
 | imagesize = 628x481px
-| noexpand  = false
+| noexpand  = true
 | titletext = So what do we do when we get to base 10? Do we use A, B, C, etc? No: Numbers larger than about 3.6 million are simply illegal.
 }}
@@ Line 11: / Line 11: @@
 ==Explanation==
 {{incomplete|Revised but needs review from an actual mathematician.  Also, are there any practical uses for factorial numbers?  Do NOT delete this tag too soon.}}
 -> There aren't any practical uses for it, mostly because it uses 9 bases, which would take many years of numerical base training.->
 A {{w|factorial}} is a product of positive integers. For instance, four factorial, written '4!', means 4×3×2×1=24.
@@ Line 22: / Line 24: @@
 The number at the top of Cueball's presentation, 353011, is 3×6! + 5×5! + 3×4! + 0×3! + 1×2! + 1×1! which gives the decimal value of 2835, the number of the comic.
-Cueball's examples of numbers written in factoradic appear as sequences [https://oeis.org/A007623 A007623] in the OEIS.
+Cueball's examples of numbers written in factored appear as sequences [https://oeis.org/A007623 A007623] in the OEIS.
 ==Transcript==