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## #1 2013-06-02 22:17:19

{7/3}
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### 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?

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

## #2 2013-06-02 22:23:58

anonimnystefy
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### Re: 2 variable function.

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

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

## #3 2013-06-02 23:12:59

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### 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.

## #4 2013-06-02 23:24:25

anonimnystefy
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### 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.

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

## #5 2013-06-03 00:55:59

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### Re: 2 variable function.

Thanks.

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

## #6 2013-06-03 00:59:24

anonimnystefy
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### Re: 2 variable function.

You're welcome.

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