QUESTION
Consider the set C(R) = {continuous functions of real numbers} and consider its subsets. Show
that C(R) is a vector space
a. Show that the set of differentiable functions is a subspace.
b. Show that the sets O of odd functions and E of even functions are subspaces.
c. Determine if the set U of functions whose definite integral over (0,1) is a subspace or
not.
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