Question: Check that is indeed a ring; that is, let ([0. 1] be the set of functions defined from the closed unit interval [0, 1] to

Check that is indeed a ring; that is, let ([0. 1]

Check that is indeed a ring; that is, let ([0. 1] be the set of functions defined from the closed unit interval [0, 1] to the real numbers that are continuous. Define the sum and product of two functions point-wise: (f +9)(x) = f(x) +g(x) and (fg)(x) = f(x)g(x). Show that CO. 1] is a commutative ring. (You may use theorems from calculus.)

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