September 29, 2023

# #2835: Factorial Numbers explain

{{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:]

[Title:]Variable-base Factoradic™ numbers

[Diagram in the form of a slip of paper, left edge torn jagged to indicate indefinite continuation]

[Several stacked elements. Following the general pattern of having “Base” at the top a base-number below that, and a square below that holding a digit (less than the given base-number)]

[Rightmost stack:] Base 2 [square:] 1

[2nd rightmost stack:] Base 3 [square:] 1

[3rd rightmost stack:] Base 4 [square:] 1

[4th rightmost stack:] Base 5 [square:] 0

[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.]

[Two column-pairs, with idential paired-headers, above (generally) a ’number’, a linking dash and another ’number']

[Left headers for both:] Base 10

[Right headers for both:] Factoradic

[First column of number pairs:]

1 — 1

2 — 10

3 — 11

4 — 20

5 — 21

6 — 100

7 — 101

[Gap]

21 — 311

22 — 320

23 — 321

[Continuation in second column of number pairs:]

24 — 1,000

25 — 1,001

[Gap]

5,038 — 654,320

5,039 — 654,321

5,040 — 1,000,000

[Gap]

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!

[Caption under the comic:] 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.