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#1 2013-06-02 00:17:19

{7/3}
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Registered: 2013-02-11
Posts: 210

2 variable function.

If f(a,b)=f(b,a) and f(a+b,c)=f(a,c)+f(b,c) then what are the solutions for f?


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#2 2013-06-02 00:23:58

anonimnystefy
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From: The Foundation
Registered: 2011-05-23
Posts: 14,861

Re: 2 variable function.

f(a,b)=k*a*b, where k is some constant.


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#3 2013-06-02 01:12:59

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: 2 variable function.

How did you derive it?


There are 10 kinds of people in the world,people who understand binary and people who don't.

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#4 2013-06-02 01:24:25

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,861

Re: 2 variable function.

Well, from the second condition f(a,b)=a*f(1,b), whoch can be proven by induction. Then, we have f(1,b)=f(b,1). And finally f(b,1)=b*f(1,1). So, f(a,b)=a*b*f(1,1) and f(1,1) can be anything we want, so, let's just call it k, where k can be any number. f(a,b)=k*a*b.


“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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#5 2013-06-02 02:55:59

{7/3}
Member
Registered: 2013-02-11
Posts: 210

Re: 2 variable function.

Thanks.


There are 10 kinds of people in the world,people who understand binary and people who don't.

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#6 2013-06-02 02:59:24

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 14,861

Re: 2 variable function.

You're welcome.


“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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