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Me too. Pretty interesting. I came here looking to get some review for hyperbolic functions for a math related project to take a math conference this Spring. Factorials are apparently rather vital in hyperbolic functions it seems.
@@juicewrld822I never learned about Double Factorials or Iterative Factorials in elementary or highschool either but these topics seem like it can be taught as early as junior year of highschool. The concepts aren't that difficult to grasp. I was already being taught introductory calculus in junior year which is way more complex than Double Factorials and Iterative Factorials.
I never learned about Double Factorials or Iterative Factorials in elementary or highschool either but these topics seem like it can be taught as early as junior year of highschool. The concepts aren't that difficult to grasp. I was already being taught introductory calculus in junior year which is way more complex than Double Factorials and Iterative Factorials.
A factorial gives you the amount of orders of choices you have when you have a sample of choices. For example, if you have 5 toys and want to know how many different orders there are of choices, you can take 5! and know that there are 120 different outcomes. (ABCDE, ACDEB, ADCEB,....., etc.) I'm not sure on a double or integrated factorials.
Any reason why the double factorial is that specific way? Like you multiply every alternate number. And similarly, is a triple factorial something you get when you multiply every third number?
If I was formulating this operation I would have prioritized not making it nearly indistinguishable from “a factorial of a factorial”. Yes you can just tell people that (4!)! Is not the same as 4!!, or you could have just made a new symbol.
All my calculators (CAS and non CAS) give different answers than in this video. For example 3! = 720 The TI-86 and HP Prime can also calculate the double factorial of a number expressed as a decimal fraction. For example 3.3!! = 262289.062411 Also GOOGLE CALCULATOR on PC desktop can do it. (Ti-89, TI-Nspire CX CAS cannot do this!)
Thank you. Love from srilanka. I want to know. when I type double Factorials in a cal. why I get a factorial's factorial. ex :- 3!! -> 720 It's like :- 3!! :- 6! :- 720
You can write double factorials using simple factorials if you take the even and odd cases apart. For the even case, (2n)!! = 2^n × n! We can show it using this : 2 × 4 × ... × (2n - 2) × 2n = 2 × 1 × 2 × 2 × ... × 2 × (n - 1) × 2 × n = 2^n × 1 × 2 × ... × n = 2^n × n! The odd case is a bit more difficult, we have (2n + 1)!! = (2n + 1)! / (2^n × n!) To show this, we write : (2n + 1)! = 1 × 2 × 3 × ... × 2n × (2n + 1) = 1 × 3 × ... × (2n + 1) × 2 × 4 × ... × 2n = (2n + 1)!! × (2n)!! Therefore, we have (2n + 1)!! = (2n + 1)! / (2n)!!, or (2n + 1)!! = (2n + 1)! / (2^n × n!)
To understand, first consider what the basic factorial n! means. It means how many possible ways a group of items can be arranged. For example, if we have 3 items: A B C then n=3. Let's find out how many ways to organize A B C in order: A B C A C B B A C B C A C A B C B A There are 6 different ways to organize a group of items A B C. Thus, 3 items can be written as _3!_ 3! = 1 × 2 × 3 3! = 6
Thus 0! and 1! Both equal to 1. For 0!, there are no possible arrangements other than one (which is "nothing"). So it's 1. For 1! there's only one possible arrangement of 1 item. And for the double factorials of 0!! and 1!! since there's only 1 possible arrangement, then the answer is also 1.
It's looks like a form of iterative factorial. Let _n_ = 3 for example: (10 - 3!)! (10 - (3×2×1))! (10 - 6)! (4)! (4 × 3 × 2 × 1) 24 Note that n in this expression cannot be larger than 4 because it would result in a negative integer and factorials can only be done with positive integers.
Is there a such thing as an exponentiative divisional factorialized factorial? Like this: 5(^/!!) = 1! ^ 1!/2! ^ 1!/2!/3! ^ 1!/2!/3!/4! ^ 1!/2!/3!/4!/5!
Factorials are only defined for natural numbers (and factors are natural numbers only)., And 0! doesn't mean 0*0=0, its different case proved by combination that 0! =1. So your 0 is not natural numbers and can't be multiplied as you stated
Damn brackets always messing things up. Sometimes theyre not there but youre supposed to pretend they are. Sometimes its the other way around. I hate you math. Damn you. lol
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I didn't know there was a thing called "double factorial" so far! Thanks so much! You deserve more and more!
Me too. Pretty interesting. I came here looking to get some review for hyperbolic functions for a math related project to take a math conference this Spring. Factorials are apparently rather vital in hyperbolic functions it seems.
Same here. I've just learned this today.
I graduated already, but feel I've learned a bit better under my personal studies(Math). No deadlines or pressures, thank you.
Never learned this in elem and high school
@Nicko Emmanuel Villacruz,
Yeah it all depends how…
🤔 *I think it’s either early or later* you start school?
@@juicewrld822I never learned about Double Factorials or Iterative Factorials in elementary or highschool either but these topics seem like it can be taught as early as junior year of highschool.
The concepts aren't that difficult to grasp. I was already being taught introductory calculus in junior year which is way more complex than Double Factorials and Iterative Factorials.
*nor
You aren't supposed to even learn factorials in elementary
Are you in eden Paradise 😢
MR. Organic Chemistry Tutor, thank you for a great video on Double Factorials.
Mac n cheese
I also thought 5!! =120!
😀😁
Ill punch you
@@ilikeanimals5015 😁
Never knew single factorials existed!! School never teach us but this is really interesting ~ thank you for teaching us 💗
What are double factorials used for?
Thank you sir. I didn't know this double and iterated factorial.
I never learned about Double Factorials or Iterative Factorials in elementary or highschool either but these topics seem like it can be taught as early as junior year of highschool.
The concepts aren't that difficult to grasp. I was already being taught introductory calculus in junior year which is way more complex than Double Factorials and Iterative Factorials.
Can you please make a video on graphing calculators?
Your Videos are really helpful 😄
thanks for teaching me about this :)
this vid helped me alot with my upcoming test
What is the functional use of a double factorial? Is there a triple factorial? A septuple factorial?
There could be an infinite amount of factorials, such as 4!!!, 7!!!!, (if you wanted) there could even be 9999!!!!!!!!!!!!!!!!
You make Comic Sans look good 😂😂
This made my day
God blessed Earth with your happening and graciousness
This is such an interesting video!
To give extra knowledge...... thanks alot
Using odd and even numbers in double factorials
Thanks a lot
This is something new I never saw .👍👍👍👍👍👍✌️✌️✌️✌️
Thanks teacher
When in practical math would a double or integrated factorial crop up? Or for that matter any factorial?
A factorial gives you the amount of orders of choices you have when you have a sample of choices. For example, if you have 5 toys and want to know how many different orders there are of choices, you can take 5! and know that there are 120 different outcomes. (ABCDE, ACDEB, ADCEB,....., etc.)
I'm not sure on a double or integrated factorials.
Well done.
(googolplex!)! Is it comperable with graham's number?
Ur awesome brother
Wow wow thank you ❤️💯🙏 I've learned
thank you
Thanks
Thank you sir😋
Man you're awesome
Any reason why the double factorial is that specific way? Like you multiply every alternate number. And similarly, is a triple factorial something you get when you multiply every third number?
If I was formulating this operation I would have prioritized not making it nearly indistinguishable from “a factorial of a factorial”. Yes you can just tell people that (4!)! Is not the same as 4!!, or you could have just made a new symbol.
You’re a saviour you know that?
Thank you so much.....pls I need your help....for a video on LENS MAKER FORMULA... calculations and explanations ...pls
All my calculators (CAS and non CAS) give different answers than in this video.
For example 3! = 720
The TI-86 and HP Prime can also calculate the double factorial of a number expressed as a decimal fraction. For example 3.3!! = 262289.062411
Also GOOGLE CALCULATOR on PC desktop can do it.
(Ti-89, TI-Nspire CX CAS cannot do this!)
That looks like a renamed wither's health bar
Thank you. Love from srilanka.
I want to know. when I type double Factorials in a cal. why I get a factorial's factorial.
ex :-
3!! -> 720
It's like :-
3!! :- 6! :- 720
OMG!!! TODAY ONLY I CAME TO KNOW THAT SOMETHING CALLED 'DOUBLE FACTORIALS' EXISTS!!!! BTW, Love from India.🇮🇳🇮🇳
🇮🇳❤🇺🇸
my calculator is giving 720 for 3!!
now integrate double factorial
You can write double factorials using simple factorials if you take the even and odd cases apart.
For the even case, (2n)!! = 2^n × n!
We can show it using this :
2 × 4 × ... × (2n - 2) × 2n = 2 × 1 × 2 × 2 × ... × 2 × (n - 1) × 2 × n
= 2^n × 1 × 2 × ... × n
= 2^n × n!
The odd case is a bit more difficult, we have (2n + 1)!! = (2n + 1)! / (2^n × n!)
To show this, we write :
(2n + 1)! = 1 × 2 × 3 × ... × 2n × (2n + 1)
= 1 × 3 × ... × (2n + 1) × 2 × 4 × ... × 2n
= (2n + 1)!! × (2n)!!
Therefore, we have (2n + 1)!! = (2n + 1)! / (2n)!!, or (2n + 1)!! = (2n + 1)! / (2^n × n!)
Do eigen values and eigenvectors
I had no idea about double factorial
This is a thing?
Interesting!
I didn't learned this during my elem and highschool day,it only exist during our cal 2
Me when I first saw double factorials:
It'll just be final answer multiplied by two!😂. I got it all wrong🤦🏻
Is triple factorial possible?
Like 6!=18
Students: Hmm..how can there be two factorials?
Legends: wait..why’s this dude so excited about 5
Number play, all very good and well but how about an example of a real world application or is it all just for theoretical bs guesswork?
10!! = 10 × 8×6×4×2 = 3840
I wonder why is there a "n x 1" on factorials, if that's neutral.
1:50
Short version.
Are we just making up nomenclature at this point?
My college professor never taught me this 🙃
(4!)! = (24)! = Very large number
Calculator got math error when calculating double factorial LOL 😁
Because the calculator probably tried to calculate 5 factorial factorial which is equal to 120!
5!!
5!!!
Tutorials
What would 0!! and 1!! be equivalent to?
To understand, first consider what the basic factorial n! means. It means how many possible ways a group of items can be arranged.
For example, if we have 3 items: A B C then n=3. Let's find out how many ways to organize A B C in order:
A B C
A C B
B A C
B C A
C A B
C B A
There are 6 different ways to organize a group of items A B C.
Thus, 3 items can be written as _3!_
3! = 1 × 2 × 3
3! = 6
Thus 0! and 1! Both equal to 1.
For 0!, there are no possible arrangements other than one (which is "nothing"). So it's 1.
For 1! there's only one possible arrangement of 1 item.
And for the double factorials of 0!! and 1!! since there's only 1 possible arrangement, then the answer is also 1.
@@_Just_Another_Guywhat about 2!! ? Would be 2?
Okay double factorial is decreasing by 2...
Who else was thinking 5!! Would be 5! × 4! × 3! × 2! × 1! ?
Meee
Double factorial is n!! = (n!)!
(10-n!)!
what's the name of that, and how to calculate it, please, anyone?
It's looks like a form of iterative factorial.
Let _n_ = 3 for example:
(10 - 3!)!
(10 - (3×2×1))!
(10 - 6)!
(4)!
(4 × 3 × 2 × 1)
24
Note that n in this expression cannot be larger than 4 because it would result in a negative integer and factorials can only be done with positive integers.
Oh! Thank you so much
@@_Just_Another_Guy
How about 0!! , is it possible?
thatd just be 1
What about triple factorial?
May be if 7!!!= 7×4×1
What about 4!! ?
4*2*0=?
I don't know!
4*2.
why is this useful?
Good question
Is there a such thing as an exponentiative divisional factorialized factorial? Like this: 5(^/!!) = 1! ^ 1!/2! ^ 1!/2!/3! ^ 1!/2!/3!/4! ^ 1!/2!/3!/4!/5!
3!!=?, 2!!=?
How would then the result look like I you have ((4!)!!)!🤔
that was unexpected
wrong write 5 !! into google and u get 198 digit number
First time I saw...
Can't 8!! Be 8*6*4*2*0 = 0
Factorials are only defined for natural numbers (and factors are natural numbers only)., And 0! doesn't mean 0*0=0, its different case proved by combination that 0! =1. So your 0 is not natural numbers and can't be multiplied as you stated
0 factorial is 1 so even if u do it it'll stay the same
U dont use 0
N!!!?
No.
No means is there any way to find double factorial
Damn brackets always messing things up. Sometimes theyre not there but youre supposed to pretend they are. Sometimes its the other way around. I hate you math. Damn you. lol
Triple factorials tho....
_WHAT’S 6 x 3?_
7!=5040
10!!=38040
(4!)!=620448401733239439360000
thanks