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    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????
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    (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?
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    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.
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    (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 ^^
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    (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.
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    (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.
    Follow the pattern
    3!=3x2x1
    2!=3x2x1/3=2x1
    1!=2x1/2=1
    0!=1/1=1.
     \displaystyle (n-1)!=\frac{n!}{n} . If n=1?
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    (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!.
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    https://youtu.be/Mfk_L4Nx2ZI

    Watch this for a clearer understanding
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    (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.
    Follow the pattern
    3!=3x2x1
    2!=3x2x1/3=2x1
    1!=2x1/2=1
    0!=1/1=1.
     \displaystyle (n-1)!=\frac{n!}{n} . 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
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    (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
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    (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
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    (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
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    (Original post by RDKGames)
    Well at least it's starting to sink in
    yup
 
 
 
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