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 ⊕.