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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Why? Can you show me an example or a proof?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

The fact is you have already seen a couple of examples. You just have not yet understood what you saw.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Can you show me one again?

Is it about numerical stability?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

When you are ready to accept it we will continue with that one. After all, it is the best example of itself. Bafflers is where the answers are.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

If I accept it you will explain it to me? Okay.Sure.3**2-2**2<>(3-2)(3+2). Everybody knows that.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Sure.3**2-2**2<>(3-2)(3+2). Everybody knows that

They do!? 5 = 5, does it not?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

But,by what you propose,it is not. That's confusing me.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

What is an identity?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

But why do you say that

a**2-b**2<>(a-b)(a+b)

if it is contradictory to the identity you just wrote above.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

What is an identity?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Something that always holds?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

That is correct. In computational mathematics that is not an identity, in ordinary algebra it is.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Why is it not an identity in comp. math? Numerical stability?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Sometimes it has to do with numerical stability and sometimes it does not.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

And when does it not?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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That was first investigated by John Von Neumann. He could not answer it fully and neither can I. Numerical analysis is the study of algorithms like that so called identity.

Incidentally, that integral, Wolfram does not know how to do it either.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

WA didn't calculate the antiderivative. It evaluated it.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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Nope, the last time I used mathematica on it the darn package did not get more than a few digits right!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

How do you know what the digits are?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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That too is done differently in numerical work than in ordinary math. We verify precision not with mathematical proof but by the double digit method or digit agreement between 2 different methods.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

But then to solve a problem like that one you would need ti find 2 methods. That's even harder.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

Who said it was easy and who says it has to be easy. That is another fallacy drummed into students and teachers. They mistakenly believe all problems are solvable in a couple of minutes and a couple of theorems. Just because all the textbook problems are like that. The truth is real world problem are usually not solvable.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,231

The truth they are hiding is that they are solvable in one command!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

Nice work. Just,hide it please.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

**#7)Find the generating function and general term (if they exist) of the sequence:**

**013467.........With the obvious increasin pattern +1,+2,+1,+2...**

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