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SMA_01
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Is this correct...proving function addition is associative?
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.
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.
Homework Statement
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.
Homework Equations
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.