Editing 2835: Factorial Numbers

{{comic
| number    = 2835
| date      = September 29, 2023
| title     = Factorial Numbers
| image     = factorial_numbers_2x.png
| imagesize = 628x481px
| 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.
}}

==Explanation==
{{incomplete|Created by a VARIABLE-BASED BOT BEING ESCORTED OUT OF THE COMPUTER SCIENCE DEPARTMENT BY SECURITY - Please change this comment when editing this page. Do NOT delete this tag too soon.}}

This comic is about the {{w|factorial number system}}, which are based on {{w|factorial|factorials}}.

In the xkcd version of this number system, the rightmost digit has a value of 1!, the second one 2! and so on (that is, the i-th digit has a value i!). That can be compared with the usual decimal system where the i-th digit has value 10^(i-1) or the binary system where the i-th digit has value 2^(i-1).

The title text discusses a "problem" with this system, in that numbers above 3,628,800 (10!) have ambiguous notation, as it can be difficult to know whether the number in this system is (10)000000000, or (1)0000000000. Some use the letters A-Z to denote such larger numbers, e.g. A000000000. However, Cueball in this comic just announces that an number above 987654321 in this number system (or 3,628,799) is illegal.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}
:Variable-base Factoradic™ numbers

:{|
|Base 7||Base 6||Base 5||Base 4||Base 3||Base 2
|-
|3||5||3||0||1||1
|}

:Left side

:{| class="wikitable"
|Base 10||Factoradic
|-
|1||1
|-
|2||10
|-
|3||11
|-
|4||20
|-
|5||21
|-
|6||100
|-
|7||101
|-
| 
|-
|21||311
|-
|22||320
|-
|23||321
|}

:Right side

:{| class="wikitable"
|Base 10||Factoradic
|-
|24||1,000
|-
|25||1,001
|-
| 
|-
|5,038||654,320
|-
|5,039||654,321
|-
|5,040||1,000,000
|-
| 
|-
|999,998||266,251,210
|-
|999,999||266,251,211
|-
|1,000,000||266,251,220
|-
|1,000,001||266,251,221
|}

:Cueball: Small numbers like seven or nineteen shouldn't use big numerals like "7" or "9".
:Cueball: I mean, "9" is the biggest numeral we have! It should be reserved for '''''big''''' numbers.
:Cueball: Small numbers should be written with small numerals like "1" or "2".
:Cueball: That's why my variable-base system uses...Hey! No, listen!

:Factorial numbers are the number system that sounds most like a prank by someone who's about to be escorted out of the math department by security.

{{comic discussion}}

[[Category:Comics featuring Cueball]]
[[Category:Characters with hats]]
[[Category:Math]]