Editing Talk:2835: Factorial Numbers
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: 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. [[User:EebstertheGreat|EebstertheGreat]] ([[User talk:EebstertheGreat|talk]]) 01:55, 30 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. [[User:EebstertheGreat|EebstertheGreat]] ([[User talk:EebstertheGreat|talk]]) 01:55, 30 September 2023 (UTC) | ||
− | : A great deal of interesting maths can be found in and around | + | : 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?! [[Special:Contributions/162.158.90.249|162.158.90.249]] 22:38, 29 September 2023 (UTC) | I thought this was a complete joke, until coming here. The "factorial number system" exists?! [[Special:Contributions/162.158.90.249|162.158.90.249]] 22:38, 29 September 2023 (UTC) | ||
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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....[[User:Alcatraz ii|Alcatraz ii]] ([[User talk:Alcatraz ii|talk]]) 01:25, 30 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....[[User:Alcatraz ii|Alcatraz ii]] ([[User talk:Alcatraz ii|talk]]) 01:25, 30 September 2023 (UTC) | ||
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Factorial base also allows to finitely represent all rational numbers - no constant base is capable of that! [[Special:Contributions/172.68.238.76|172.68.238.76]] 01:55, 30 September 2023 (UTC) | Factorial base also allows to finitely represent all rational numbers - no constant base is capable of that! [[Special:Contributions/172.68.238.76|172.68.238.76]] 01:55, 30 September 2023 (UTC) | ||
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I feel like Michael when Oscar is trying to explain what a “surplus” is.[[Special:Contributions/162.158.186.241|162.158.186.241]] 04:12, 30 September 2023 (UTC) | I feel like Michael when Oscar is trying to explain what a “surplus” is.[[Special:Contributions/162.158.186.241|162.158.186.241]] 04:12, 30 September 2023 (UTC) | ||
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== The warning is complete nonsense, just remove it == | == The warning is complete nonsense, just remove it == | ||
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:::<nowiki>*</nowiki>sigh* As has been stated, you MUST be new here. The "incomplete" tag goes on new comics while their descriptions are still in flux. When the bot creates the empty description page, it does so with the Incomplete warning, labelled with its name. On the first edit, someone ALWAYS changes the name to some silly gag that's related to the comic, often pretending it's the name of the bot that created the page for us. In this case the comic shows Cueball being escorted out, so the joke is the bot is being escorted out. If you're not going to have a sense of humour, why are you here? Just leave the editing to others in the meantime. :) (Oh, and as the user above noted, make sure to end your comments with <nowiki>~~~~</nowiki> (4 tildes), like it says at the top of the editing text box you type in). :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:13, 1 October 2023 (UTC) | :::<nowiki>*</nowiki>sigh* As has been stated, you MUST be new here. The "incomplete" tag goes on new comics while their descriptions are still in flux. When the bot creates the empty description page, it does so with the Incomplete warning, labelled with its name. On the first edit, someone ALWAYS changes the name to some silly gag that's related to the comic, often pretending it's the name of the bot that created the page for us. In this case the comic shows Cueball being escorted out, so the joke is the bot is being escorted out. If you're not going to have a sense of humour, why are you here? Just leave the editing to others in the meantime. :) (Oh, and as the user above noted, make sure to end your comments with <nowiki>~~~~</nowiki> (4 tildes), like it says at the top of the editing text box you type in). :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:13, 1 October 2023 (UTC) | ||
:Okay, now the Incomplete warning needs to stay up forever. :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:13, 1 October 2023 (UTC) | :Okay, now the Incomplete warning needs to stay up forever. :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 05:13, 1 October 2023 (UTC) | ||
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== The "adic" part of factor-adic numbers == | == The "adic" part of factor-adic numbers == | ||
− | It's not explicitly mentioned in the comic but the "adic" in the name "Factor''adic''™" implies that the number system extends the factorial number system by being in some way "adic" as discussed in [https:// | + | It's not explicitly mentioned in the comic but the "adic" in the name "Factor''adic''™" implies that the number system extends the factorial number system by being in some way "adic" as discussed in [https://youtu.be/tRaq4aYPzCc 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) |
: The "adic" in factoradic doesn't actually relate to p-adic numbers of any kind. Rather, both factoradic and p-adic numbers use the suffix -adic to refer to the concept of adicity, which is "The number of arguments or operands a function or operation takes" according to Wiktionary. Each place value of a p-adic number had p possibilities, and each place value in the factoradic system has a number of possible arguments determined by the factorial of the place. Factoradic would be better called "factorary" since it's more similar to ordinary n-ary number systems, but I guess it just isn't. [[Special:Contributions/172.69.205.130|172.69.205.130]] 20:43, 30 September 2023 (UTC) | : The "adic" in factoradic doesn't actually relate to p-adic numbers of any kind. Rather, both factoradic and p-adic numbers use the suffix -adic to refer to the concept of adicity, which is "The number of arguments or operands a function or operation takes" according to Wiktionary. Each place value of a p-adic number had p possibilities, and each place value in the factoradic system has a number of possible arguments determined by the factorial of the place. Factoradic would be better called "factorary" since it's more similar to ordinary n-ary number systems, but I guess it just isn't. [[Special:Contributions/172.69.205.130|172.69.205.130]] 20:43, 30 September 2023 (UTC) | ||
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== Title text == | == Title text == | ||
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It returns an array (@-variable, in Perl) of digits, in standard most-to-least-significance order, that you can convert to a glyphwise notation in any way that you wish (or do a string conversion within the function, at each stage of building it up). ...and I'm presenting a ''slightly'' less optimised version of it here (some of the Perl-tricks I originally used don't translate well into some non-Perl) and, yes, the <code>while ($n>=$base)</code> loop could be done using modulus and integer-division, but it's a fairly trivial part of the looping process.<br /> | It returns an array (@-variable, in Perl) of digits, in standard most-to-least-significance order, that you can convert to a glyphwise notation in any way that you wish (or do a string conversion within the function, at each stage of building it up). ...and I'm presenting a ''slightly'' less optimised version of it here (some of the Perl-tricks I originally used don't translate well into some non-Perl) and, yes, the <code>while ($n>=$base)</code> loop could be done using modulus and integer-division, but it's a fairly trivial part of the looping process.<br /> | ||
If you have any ''real'' problems with it, it's probably going to be if you're hitting any recursion-depth limits (especially as it uses roughly twice as many recursive calls as the eventual notation-length it produces). I also have a 'stack-based' version (loops round as it shifts in enough 'slots', then works back down again assigning the place-values) which avoids such trouble, but that's coded in a slightly esoteric Perlish way that I'm not sure most of you'd appreciate. ;) [[Special:Contributions/141.101.76.77|141.101.76.77]] 20:25, 30 September 2023 (UTC) | If you have any ''real'' problems with it, it's probably going to be if you're hitting any recursion-depth limits (especially as it uses roughly twice as many recursive calls as the eventual notation-length it produces). I also have a 'stack-based' version (loops round as it shifts in enough 'slots', then works back down again assigning the place-values) which avoids such trouble, but that's coded in a slightly esoteric Perlish way that I'm not sure most of you'd appreciate. ;) [[Special:Contributions/141.101.76.77|141.101.76.77]] 20:25, 30 September 2023 (UTC) | ||
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Factorial numbers is new to me... It sounds more like a coding system than a number system, LOL! "The door code is 4503 in factorial! Figure it out!" (I'd write this on the bottom of the comments as usual, but I don't want to get mixed up with that ill-thought out and unsigned coding sample Algorithm and table that I KNOW must be mangled when published because the wiki refuses to honour single Newlines. Clearly the author didn't take a peek at what it looks like when published EDIT: Correction, wow, the wiki spotted the code and marked it as such automatically (for now), wow!) :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 04:59, 1 October 2023 (UTC) | Factorial numbers is new to me... It sounds more like a coding system than a number system, LOL! "The door code is 4503 in factorial! Figure it out!" (I'd write this on the bottom of the comments as usual, but I don't want to get mixed up with that ill-thought out and unsigned coding sample Algorithm and table that I KNOW must be mangled when published because the wiki refuses to honour single Newlines. Clearly the author didn't take a peek at what it looks like when published EDIT: Correction, wow, the wiki spotted the code and marked it as such automatically (for now), wow!) :) [[User:NiceGuy1|NiceGuy1]] ([[User talk:NiceGuy1|talk]]) 04:59, 1 October 2023 (UTC) | ||
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== Factoradic Algorithms == | == Factoradic Algorithms == | ||
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perform this in one or two lines, where as a language like c++ will be longer. | perform this in one or two lines, where as a language like c++ will be longer. | ||
− | The simplest algorithm is to generate the digits from right to left one at time by dividing the number by | + | The simplest algorithm is to generate the digits from right to left one at time by dividing the number by the radix until the quotient reaches zero: |
#include <iostream> | #include <iostream> | ||
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int factoradic(int num) { | int factoradic(int num) { | ||
string digits; | string digits; | ||
− | int radix = 2; | + | int radix = 2, quote = 0, remainder = 0; |
− | + | do { | |
− | + | quote = num / radix; | |
− | num | + | remainder = num % radix; |
− | } | + | num = quote; radix++; |
+ | digits.push_back(to_string(remainder)[0]); | ||
+ | } while (quote != 0); | ||
reverse(digits.begin(), digits.end()); | reverse(digits.begin(), digits.end()); | ||
return atoi(digits.c_str()); | return atoi(digits.c_str()); | ||
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int main(int argc, char* argv[]) { | int main(int argc, char* argv[]) { | ||
− | for (int i = | + | for (int i = 1; i < 26; i++) |
cout<<i<<" - "<<factoradic(i)<<endl; | cout<<i<<" - "<<factoradic(i)<<endl; | ||
for (int i = 5038; i < 5042; i++) | for (int i = 5038; i < 5042; i++) | ||
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1000000 - 266251220 | 1000000 - 266251220 | ||
1000001 - 266251221 | 1000001 - 266251221 | ||
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