Factorial

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Dipika
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Factorial

Unread post by Dipika » Thu Dec 22, 2011 11:28 am

Need the proof of 0!=1

tanvirab
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Re: Factorial

Unread post by tanvirab » Thu Dec 22, 2011 1:57 pm

There is no proof, it's a definition.

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sm.joty
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Re: Factorial

Unread post by sm.joty » Thu Dec 22, 2011 2:23 pm

একটা বস্তুর মধ্য থেকে একটা বস্তু একভাবেই নেয়া যায়। এবার সমাবেশ এর সুত্র ব্যবহার করে দেখ।
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........

photon
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Re: Factorial

Unread post by photon » Thu Dec 22, 2011 7:50 pm

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
$O! = 1!/1=1$
Try not to become a man of success but rather to become a man of value.-Albert Einstein

tanvirab
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Re: Factorial

Unread post by tanvirab » Fri Dec 23, 2011 12:23 am

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.

raihan khan
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Re: Factorial

Unread post by raihan khan » Tue Jan 03, 2012 9:58 pm

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

tanvirab
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Re: Factorial

Unread post by tanvirab » Tue Jan 03, 2012 10:38 pm

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.

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