Let G be the set of all functions f :[0,1]R. For f,gG define the function fg by setting f g (x) := f (x) + g (x) (i) Explain what it means that two...

1.

Let G be the set of all functions f :[0,1]→R. For f,g∈G define the function f⊕g by setting

f ⊕ g (x) := f (x) + g (x)

(i) Explain what it means that two functions f : [0,1] → R and g : [0,1] → R are

for x ∈ [0,1].

equal, so explain the meaning of f = g.

(ii) Show that G is a group with respect to ⊕.