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#1 2013-11-18 08:48:53

ShivamS
Member
Registered: 2011-02-07
Posts: 3,440

Mathematica - proving something

How do I prove


using Mathematica 9?
Is an inductive proof even possible in Mathematica?

Last edited by ShivamS (2013-11-18 08:49:44)

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#2 2013-11-18 09:03:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Mathematica - proving something

Hi;

Mathematica already knows that is true but to do the steps

For the base case.

1^2==(n*(n + 1) (2 n + 1))/6 /.n->1

True



For the inductive step:

If that is true then

ought to be true. Subtract 1). from 2).

((n*(n + 1) (2 n + 1))/6 /. n -> n + 1) - (n*(n + 1) (2 n + 1))/6 // FullSimplify

(n+1)^2

The LHS is obviously (n+1)^2 so we are done.


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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#3 2013-11-18 09:09:10

ShivamS
Member
Registered: 2011-02-07
Posts: 3,440

Re: Mathematica - proving something

The first statement doesn't compute properly...

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#4 2013-11-18 09:10:07

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Mathematica - proving something

Hi;

Change the = to ==, I am sorry.


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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#5 2013-11-18 09:12:33

ShivamS
Member
Registered: 2011-02-07
Posts: 3,440

Re: Mathematica - proving something

Ok, thanks.

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#6 2013-11-18 09:14:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Mathematica - proving something

Hi;

I have made lots of changes to post #2.

Mathematica knows that sum:

Sum[k^2, {k, 1, n}]

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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#7 2013-11-18 09:46:06

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Mathematica - proving something

Sum[...,{i,1,n}]

seems to be a bit faster than

Sum[...,{i,n}]

Why's 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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#8 2013-11-18 10:02:01

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Mathematica - proving something

I guess because he needs time to figure the lower index.


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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#9 2013-11-18 10:06:55

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Mathematica - proving something

But, it's an 0.03s difference.

Last edited by anonimnystefy (2013-11-18 10:07:16)


“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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#10 2013-11-18 10:10:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Mathematica - proving something

If it is not granularity, then that is probably the amount of time it would take.


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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#11 2013-11-18 11:32:33

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Mathematica - proving something

Granularity?


“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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#12 2013-11-18 11:40:26

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Mathematica - proving something

Trying to measure a very small increment with a large measuring stick produces granularity.


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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#13 2013-11-18 12:16:08

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Mathematica - proving something

How does that happen in M. Do you have an example?


“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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#14 2013-11-18 22:10:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Mathematica - proving something

I do not think I can.  If you only have a 3 ft. stick and you and I both try to measure on inch, the measurements will vary greatly.


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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#15 2013-11-18 22:12:16

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,860

Re: Mathematica - proving something

I do not think that is the problem.


“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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#16 2013-11-18 22:19:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Mathematica - proving something

Then I would go with the fact that it has to make one more decision.


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.

Offline

#17 2013-12-09 13:58:12

ShivamS
Member
Registered: 2011-02-07
Posts: 3,440

Re: Mathematica - proving something

Thanks for fixing it.

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#18 2013-12-09 21:47:29

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 82,610

Re: Mathematica - proving something

Hi;

You are welcome.


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.

Offline

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