(adsbygoogle = window.adsbygoogle || []).push({}); Is this correct...proving function addition is associative???

1. The problem statement, all variables and given/known data

Let F be the set of all real-valued functions having as domain the set ℝ of all real number. Prove that function addition + on F is associative.

2. Relevant equations

3. The attempt at a solution

I'm not sure if I approached this correctly, but here is how I did it:

For all f,g,h in F:

(f+g)(x)+h(x)

=f(x)+g(x)+h(x) [by definition of function addition]

and

f(x)+(g+h)(x)

=f(x)+g(x)+h(x) [by definition of function addition]

so that, (f+g)(x)+h(x)=f(x)+(g+h)(x) for all x in ℝ

Did I do this correctly? Any help is appreciated, thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Is this correct proving function addition is associative?

**Physics Forums | Science Articles, Homework Help, Discussion**