Factorial
Factorial
Need the proof of 0!=1
Re: Factorial
There is no proof, it's a definition.
Re: Factorial
একটা বস্তুর মধ্য থেকে একটা বস্তু একভাবেই নেয়া যায়। এবার সমাবেশ এর সুত্র ব্যবহার করে দেখ।
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধাবিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
তবুও এগিয়ে যেতে হবে.........
বাধাবিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
Re: Factorial
my teacher once gave me that Proof( not by me0,
$n! =n(n1)!$
Or,$(n1)! = n(n1)!/n =n!/n$
Putting n = 1, we have
$O! = 1!/1=1$
$n! =n(n1)!$
Or,$(n1)! = n(n1)!/n =n!/n$
Putting n = 1, we have
$O! = 1!/1=1$
Try not to become a man of success but rather to become a man of value.Albert Einstein
Re: Factorial
Here you need to define $1!$ first. This is also acceptable. But usually $0!$ is defined first then all the other positive integer factorials are derived from it.photon wrote:my teacher once gave me that Proof( not by me0,
$n! =n(n1)!$
Or,$(n1)! = n(n1)!/n =n!/n$
Putting n = 1, we have
$O! = 1!/1=1$

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Re: Factorial
actually n things can be per mutated by n! if n is zero there is only one way to permute and it is i cannot permute. so 0!=1
Re: Factorial
No, that's not a good definition. Because,
$n! = (n1)! * n$ where $n > 0$ and one initial value. Usually the initial value is taken as $0! = 1$. But you can take any initial value.
does not mean anything until you have defined what $n!$ is. So you need to define factorial first. Which is done by,raihan khan wrote:n things can be per mutated by n!
$n! = (n1)! * n$ where $n > 0$ and one initial value. Usually the initial value is taken as $0! = 1$. But you can take any initial value.