Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

Login

Username

Password

Not registered yet?

#1 2013-06-02 22:17:19

{7/3}
Full Member

Offline

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
Real Member

Offline

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

{7/3}
Full Member

Offline

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
Real Member

Offline

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

{7/3}
Full Member

Offline

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
Real Member

Offline

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

Board footer

Powered by FluxBB