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# For my own piece of mind(factorials)

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1. Why does 0!=1 ?

sure the factorial(to me anyway) means sum of all the numbers multiplied from 1 to itself

so 1! would be just 1

2! would be 1x2
3! would be 1x2x3

but how can 0!=1????
2. (Original post by thegreatwhale;[url="tel:66467056")
66467056[/url]]Why does 0!=1 ?

sure the factorial(to me anyway) means sum of all the numbers multiplied from 1 to itself

so 1! would be just 1

2! would be 1x2
3! would be 1x2x3

but how can 0!=1????
Factorial means the amount of ways to arrange n number of objects. So how many ways are there to arrange 0 objects?
3. Intuition: if you accept that x! = x(x-1)!, then by letting x = 1,
1! = 1(0!)
And then 1! = 1, so
1 = 1(0!)
1 = 0!

In reality, 0! is defined to be 1, and then x! = x(x-1)!, for all other x.
4. (Original post by RDKGames)
Factorial means the amount of ways to arrange n number of objects. So how many ways are there to arrange 0 objects?
0 because nothing exists there what tf?
you can't arrange what's not there
(Original post by Alex:)
Intuition: if you accept that x! = x(x-1)!, then by letting x = 1,
1! = 1(0!)
And then 1! = 1, so
1 = 1(0!)
1 = 0!

In reality, 0! is defined to be 1, and then x! = x(x-1)!, for all other x.
not understanding any of this ^^
5. (Original post by thegreatwhale;[url="tel:66467412")
66467412[/url]]0 because nothing exists there what tf?
you can't arrange what's not there

not understanding any of this ^^
Yes you can. There is one way to arrange them, which is the absence of them.
6. (Original post by thegreatwhale)
0 because nothing exists there what tf?
you can't arrange what's not there

not understanding any of this ^^
You can arrange 0 objects in one way.
3!=3x2x1
2!=3x2x1/3=2x1
1!=2x1/2=1
0!=1/1=1.
. If n=1?
7. (Original post by thegreatwhale)
0 because nothing exists there what tf?
you can't arrange what's not there

not understanding any of this ^^
So by definition,
x! = 1 if x = 0
x! = x (x-1)! if x > 0
It's defined this way, just like how the trig functions are defined by power series. But if we just take the relation x! = x(x-1)! for intuition:

You know that,
4! = 4 * 3!
3! = 3 * 2!
2! = 2 * 1!
1! = 1 * 0!
and the last line only 'makes sense' if 0! = 1. And like my previous post, we can insert x = 1 into the relation to get
1! = 0!.
8. https://youtu.be/Mfk_L4Nx2ZI

Watch this for a clearer understanding
9. (Original post by RDKGames)
Yes you can. There is one way to arrange them, which is the absence of them.
doesn't sit well with my logic but i guess so....
(Original post by B_9710)
You can arrange 0 objects in one way.
3!=3x2x1
2!=3x2x1/3=2x1
1!=2x1/2=1
0!=1/1=1.
. If n=1?
ok
(Original post by Alex:)
So by definition,
x! = 1 if x = 0
x! = x (x-1)! if x > 0
It's defined this way, just like how the trig functions are defined by power series. But if we just take the relation x! = x(x-1)! for intuition:

You know that,
4! = 4 * 3!
3! = 3 * 2!
2! = 2 * 1!
1! = 1 * 0!
and the last line only 'makes sense' if 0! = 1. And like my previous post, we can insert x = 1 into the relation to get
1! = 0!.
thanks
(Original post by RDKGames)
https://youtu.be/Mfk_L4Nx2ZI

Watch this for a clearer understanding
he explained it but i'm not "convinced" but i guess it's the best simple explanation there is
10. (Original post by thegreatwhale;[url="tel:66467922")
66467922[/url]]doesn't sit well with my logic but i guess so....

ok

thanks

he explained it but i'm not "convinced" but i guess it's the best simple explanation there is
If you are not convinced by that then you are not convinced on what factorials really are
11. (Original post by RDKGames)
If you are not convinced by that then you are not convinced on what factorials really are
even though i do philosophy it's slowly seeping in i think i'm slowly getting it.... just one of those things you gotta think about for a long time haha
12. (Original post by thegreatwhale;[url="tel:66468090")
66468090[/url]]even though i do philosophy it's slowly seeping in i think i'm slowly getting it.... just one of those things you gotta think about for a long time haha
Well at least it's starting to sink in
13. (Original post by RDKGames)
Well at least it's starting to sink in
yup

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