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#326 2012-02-17 08:36:13

bobbym
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Re: Limits!

Correct! Wanted to see if you were sure.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#327 2012-02-17 08:36:49

anonimnystefy
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Re: Limits!

tongue you sneaky little... big_smile


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#328 2012-02-17 08:43:53

bobbym
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Re: Limits!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#329 2012-02-17 09:00:18

anonimnystefy
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Re: Limits!

hi bobbym


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#330 2012-02-17 09:03:22

bobbym
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Re: Limits!

Correct!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#331 2012-02-17 09:06:09

anonimnystefy
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Re: Limits!

hi bobbym



why are you giving these easy ones?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#332 2012-02-17 09:10:59

bobbym
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Re: Limits!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#333 2012-02-17 09:17:09

anonimnystefy
Real Member

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Re: Limits!

hi bobbym


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#334 2012-02-17 09:17:48

bobbym
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Re: Limits!

Not true.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#335 2012-02-17 09:35:24

anonimnystefy
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Re: Limits!

no?but wolfram said that they don't converge.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#336 2012-02-17 09:36:49

bobbym
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Re: Limits!

What did you enter?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#337 2012-02-17 09:45:12

anonimnystefy
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Re: Limits!

is the ans 0?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#338 2012-02-17 09:46:54

bobbym
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Re: Limits!

Yes, and there is a very good argument for that.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#339 2012-02-17 09:50:49

anonimnystefy
Real Member

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Re: Limits!

and that is?


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#340 2012-02-17 09:57:27

bobbym
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Re: Limits!

Do you agree that we can write the above limit in this more convenient form:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#341 2012-02-17 10:03:51

anonimnystefy
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Re: Limits!

yes...


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#342 2012-02-17 10:07:53

bobbym
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Re: Limits!

Have you heard of Stirling's formula or approximation?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#343 2012-02-17 10:14:42

anonimnystefy
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Re: Limits!

no,but i know that e^n is O(n^(n+1/2)) big_smile


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#344 2012-02-17 10:19:16

bobbym
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Re: Limits!

Okay, Stirling's formula was discovered by James Stirling and is a very good approximation for factorials. It is used quite often in many fields of mathematiocs.

1)First convince yourself that



f(100) is a good approximation of 100!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#345 2012-02-17 10:33:21

anonimnystefy
Real Member

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Re: Limits!

ok


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#346 2012-02-17 10:41:34

bobbym
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Re: Limits!

Now it is important to understand that



but more importantly



This means that Stirling's formula becomes a better and better approximation of n! the larger n gets.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#347 2012-02-17 10:43:57

anonimnystefy
Real Member

Offline

Re: Limits!

ok.


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#348 2012-02-17 10:46:45

bobbym
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Re: Limits!

Remember the result in #340?



and Stirlings formula?



Does not the RHS of 1) look like the LHS of 2 inverted?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

#349 2012-02-17 10:49:24

anonimnystefy
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Re: Limits!

it does.so our limit is:

Last edited by anonimnystefy (2012-02-17 10:49:51)


The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
 

#350 2012-02-17 10:52:32

bobbym
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Re: Limits!

That is close:




In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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