Talk:2835: Factorial Numbers

Number systems aren't real math, at least not serious math. They're an affectation. 99.9% of math is number-system-independent, so nobody should care about them. 172.70.46.108 22:30, 29 September 2023 (UTC)

Of course it's "real math." There aren't that many applications, but so what? Math isn't about applications. Besides, there are some. Maybe not specifically for factorial base, but for some place systems. The only thing "dirty" about decimal is the arbitrariness of ten. Considering place systems in general is just considering special kinds of sums. Certainly, "serious" mathematicians are interested in proving numbers normal in specific bases, or in every base. EebstertheGreat (talk) 01:55, 30 September 2023 (UTC)

A great deal of interesting maths can be found in and around the various arrangements of digits in numbers systems, surely. AzureArmageddon 07:54, 30 September 2023 (UTC)

I thought this was a complete joke, until coming here. The "factorial number system" exists?! 162.158.90.249 22:38, 29 September 2023 (UTC)

I wanted to add a link to a converter, but the one I found is https://www.dcode.fr/factorial-base which is quite ugly with lots of adds and a bit counter-intuitive.--Pere prlpz (talk) 23:42, 29 September 2023 (UTC)

This needs simplifying a bit. Came here because I had no idea what was going on, and after a quick scroll through the prose, the main thing I learned was "it's 'cause you're dumb". May be true but I still don't get what Randall's factorial system is....Alcatraz ii (talk) 01:25, 30 September 2023 (UTC)

Factorial base also allows to finitely represent all rational numbers - no constant base is capable of that! 172.68.238.76 01:55, 30 September 2023 (UTC)

Unless you use a division sign. But yes, only radix numerals of a variable base with infinite series of factors of every prime can even theoretically finitely represent arbitrary rationals without invoking existential quantifiers. 172.71.147.26 06:43, 30 September 2023 (UTC)

I feel like Michael when Oscar is trying to explain what a “surplus” is.162.158.186.241 04:12, 30 September 2023 (UTC)

The warning is complete nonsense, just remove it

bots cant be escorted out of somewhere just remove the stupid warning 162.158.203.109 04:28, 30 September 2023 (UTC)

you must be new here - 108.162.216.143 15:51, 30 September 2023 (UTC)

The nonsense is part of the fun. AzureArmageddon 07:52, 30 September 2023 (UTC)

im deleting it

The "adic" part of factor-adic numbers

It's not explicitly mentioned in the comic but the "adic" in the name "Factoradic™" implies that the number system extends the factorial number system by being in some way "adic" as discussed in this YouTube video on the Veritasium channel and so negative numbers would have a truly wacky representation that violates the intent of the title text's pronouncement by requiring an infinitely long representation requiring infinite digits (1, 2, 3, 4, ..., 9, A, B, C, ..., infinite digits). AzureArmageddon 08:00, 30 September 2023 (UTC)

Title text

The title text references that 10! = 3,628,800 (base 10), and so for numbers greater than or equal to that, you would have to add a tenth digit in order to display them in this system. The question is asking whether you would then proceed to using letters of the alphabet such as one does in hexadecimal to which the reply is that numbers above this amount are simply illegal. The trouble comes when you try to write down the number 10 * 10! = 36,288,000 (base 10) in this system. For 10!, the notation is 1000000000 , so 9 * 10! would be 9000000000, and then to get 10 * 10!, you would have to write A000000000 because 10 * 10! < 11!. In fact, since this is the first "illegal" number, you could "legally" allow up to 10 * 10! - 1 = 36,287,999 (base 10) in the system (which would be written as 9987654321 = 9 * 10! + 9 * 9! + 8 * 8! + ... + 2 * 1! + 1 * 1!) without the need to introduce any letters. I also want to point out that the reference in the comic to 9 being reserved for big numbers is due to no number needing a 9 to write it down in this system until 9 * 9! = 3265920 which is written 900000000. Since numbers above 10! are not allowed, this means that only the 9! digit is legally allowed to hold a 9, and it only applies to numbers in that high range of 3265920 to 3628799.172.71.166.230 15:01, 30 September 2023 (UTC)

I feel the current in-Explanation explanation about that already covers this, with the addition of the validity that the digit that could need to be >9 could still be any digit 0..9 without needing to invoke the 11th digit. (Maybe a few tweaks, but not sure what you're trying to add here.) 172.70.86.148 15:13, 30 September 2023 (UTC)