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Factorial
Posted: Thu Dec 22, 2011 11:28 am
by Dipika
Need the proof of 0!=1
Re: Factorial
Posted: Thu Dec 22, 2011 1:57 pm
by tanvirab
There is no proof, it's a definition.
Re: Factorial
Posted: Thu Dec 22, 2011 2:23 pm
by sm.joty
একটা বস্তুর মধ্য থেকে একটা বস্তু একভাবেই নেয়া যায়। এবার সমাবেশ এর সুত্র ব্যবহার করে দেখ।
Re: Factorial
Posted: Thu Dec 22, 2011 7:50 pm
by photon
my teacher once gave me that Proof( not by me0,
$n! =n(n-1)!$
Or,$(n-1)! = n(n-1)!/n =n!/n$
Putting n = 1, we have
$O! = 1!/1=1$
Re: Factorial
Posted: Fri Dec 23, 2011 12:23 am
by tanvirab
photon wrote:my teacher once gave me that Proof( not by me0,
$n! =n(n-1)!$
Or,$(n-1)! = n(n-1)!/n =n!/n$
Putting n = 1, we have
$O! = 1!/1=1$
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.
Re: Factorial
Posted: Tue Jan 03, 2012 9:58 pm
by raihan khan
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
Posted: Tue Jan 03, 2012 10:38 pm
by tanvirab
No, that's not a good definition. Because,
raihan khan wrote:n things can be per mutated by n!
does not mean anything until you have defined what $n!$ is. So you need to define factorial first. Which is done by,
$n! = (n-1)! * n$ where $n > 0$ and one initial value. Usually the initial value is taken as $0! = 1$. But you can take any initial value.