(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.

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# Homework Help: Is this correct proving function addition is associative?

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