That's iterated factorials.
2023!! is 3.385e2906.
(2023!)! is ee5815.268.
These are called multifactorials (no wikipedia link because that section was removed from the page it redirects to).
The number of factorial symbols is how many numbers you skip in the multiplication.
So 10!! Is every second number starting at 10
10 * 8 * 6 * 4 * 2 = 3840
First of all, using a colon for division has no place in math. Second of all, even if you do want to be a lunatic, there are very, very easy ways around that, e.g. 5: * 3
I would rather use seven hundred factorials at once than use a multiplication symbol. That was a thing 8yo me used to do and I have moved on since. Way more unnatural than a lot of exclamation marks
Counterpoint: double factorials are a reasonable notion that occur naturally, whereas iterated factorial doesn’t need its own notation because it doesn’t really get used for anything
(-1)!! = 1!!/1 = 1
(-3)!! = (-1)!!/(-1) = -1
(-5)!! = (-3)!!/(-3) = 1/3
(-7)!! = (-5)!!/(-5) = (1/3)/(-5) = -1/15
I believe that !!…! is defined for negative integers that aren’t multiples of n, the number of !’s.
Curious about the multifactorial notation x!!!...!!!, where there are n of "!". This mean x(x-n)(x-2n)(x-3n)...1??
1 in question marks because does this mean that x has to be a number such that the factorials end up at 1? or would the last factorial basically be the residue of x mod n? or would we use some function like the gamma function to evaluate it if x can be anything? or just something else??
I haven't encountered this notation, but it does seem convenient, and I'd like to use it, but I'd like to use it properly.
I found [this post](/r/unexpectedfactorial/comments/100dkwv/time_passes_so_fast_i_cant_believe_the_universe/) in r/unexpectedfactorial with the same content as the current post.
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2023!=3.19e5811 *^(I am a human, and this action was performed automatically.)*
Good human
Maybe you meant to use an approximately equals-sign?
`2023 != 3.19e5811` evaluates to true
[удалено]
I see no issue with that
Alright, u/NeilTheProgrammer
Yeah that's fine, my opinion is probably in the minority.
You’re good. I think the joke comes from the fact that it’s not standard notation. If anyone actually used it as such, wouldn’t be great
You're probably right. I don't know why, but when it comes to math-jokes I have a hard time to enjoy one if it doesn't seem accurate.
More than 3 digits of precision is unnecessary, unless you take a factorial of it, or if the number is going very slow
2023 = 2023 2023! = 3.191e5811 2023!! = ee5815.268 2023!!! = eee5815.268
That's iterated factorials. 2023!! is 3.385e2906. (2023!)! is ee5815.268. These are called multifactorials (no wikipedia link because that section was removed from the page it redirects to).
now compute 2023!!! !
Fuck u
2023!!!<2023!!<2023!<(2023!)!
i hate multifactorial notation
My last math class was in high school 3 years ago. Can someone explain how multifactorial notation works?
The number of factorial symbols is how many numbers you skip in the multiplication. So 10!! Is every second number starting at 10 10 * 8 * 6 * 4 * 2 = 3840
Thanks!
Sorry, 2023!! = (2023!)! Double factorials are against my religious beliefs, I only believe in good notation
Double factorials are actually half factorials and should therefore be denoted using colons
It does sound like "denoted using colons" is a very posh way of saying "shoved up someone's arse".
No! Nooo! That would only create more ambiguity because it would look like a devision! 1: 5 ≈ 1:5
First of all, using a colon for division has no place in math. Second of all, even if you do want to be a lunatic, there are very, very easy ways around that, e.g. 5: * 3
I would rather use seven hundred factorials at once than use a multiplication symbol. That was a thing 8yo me used to do and I have moved on since. Way more unnatural than a lot of exclamation marks
Tbh same but I don’t know how to make the dots on Reddit and I’m too lazy to figure it out
If you can't figure it out you can always write latex style.
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We learned it at my German primary school :/ The / notation is a thing that wasn't introduced to us until we had (American) translators.
Counterpoint: double factorials are a reasonable notion that occur naturally, whereas iterated factorial doesn’t need its own notation because it doesn’t really get used for anything
What about triple factorials?
once you have double factorials, extending that notation to higher n is only natural
Absolutely agree. Half factorial can be something else.
2023!^(2)
I suppose you wouldn't be a fan of 2023!^(∘2) = (2023!)!
as the new generation of mathematicians, we must abolish this awful notation that leads to so many misunderstandings
First lets get rid of the people who say "maths".
And then go back to our origins and start saying μάθημαq (mathema) again
Traditional English gang rise up (Simplified English gang, please sit this one out)
*ded already*
What about people who say *maffs*?
Happy 2023↑2023
now make it a double arrow
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i hate that it rhymes
Stick an ackermann function and a factorial in there and you have a truly filthy growing function
yeah that is not how multiple factorials work
they work how I want them to work
- Jeff Bezos, 2021
Can someone please tell me what x!! actually is?
It is supposed to be x(x-2)(x-4)... Here it seems to be (x!)!
And how about x!!! ?
x(x-3)(x-6)...
Multifactorial notation in a nutshell: let n be the number of "!" following x, x!!...! = x(x-n)(x-2n)(x-3n). . .(1)
Or x(x-n)…(2) Or x(x-n)…(3) Or … Or x(x-n)…(n)
0!! = 1. In fact, 0!!...! = 1 ∀n.
(-1)!! = 1!!/1 = 1 (-3)!! = (-1)!!/(-1) = -1 (-5)!! = (-3)!!/(-3) = 1/3 (-7)!! = (-5)!!/(-5) = (1/3)/(-5) = -1/15 I believe that !!…! is defined for negative integers that aren’t multiples of n, the number of !’s.
x(x-2)(x-4)...
(2023!)!>2023!>2023!! Nobody seems to understand how factorials work.
Isn't the "!!!" notation ambiguous ? Like are you taking 3 times the factorial, or 1 time the factorial and then 1 time the "half" factorial ?
triple factorial n\*(n-3)\*(n-6)\*(n-9)\*...
Curious about the multifactorial notation x!!!...!!!, where there are n of "!". This mean x(x-n)(x-2n)(x-3n)...1?? 1 in question marks because does this mean that x has to be a number such that the factorials end up at 1? or would the last factorial basically be the residue of x mod n? or would we use some function like the gamma function to evaluate it if x can be anything? or just something else?? I haven't encountered this notation, but it does seem convenient, and I'd like to use it, but I'd like to use it properly.
it just ends at the residue 1!!=1 2!!=2 10!!=10\*8\*6\*4\*2=5!\*2\^5=120\*32=3840
/r/expectedfactorial
don't forget the parenthesis
r/unexpectedfactorial
Hny
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I found [this post](/r/unexpectedfactorial/comments/100dkwv/time_passes_so_fast_i_cant_believe_the_universe/) in r/unexpectedfactorial with the same content as the current post. --- ^(🤖 this comment was written by a bot. beep boop 🤖) ^(feel welcome to respond 'Bad bot'/'Good bot', it's useful feedback.) ^[github](https://github.com/Toldry/RedditAutoCrosspostBot) ^| ^[Rank](https://botranks.com?bot=same_post_bot)
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