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  3. 1 let cr be the ring of all continuous functions...

Question: 1 let cr be the ring of all continuous functions...

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1. Let C(R) be the ring of all continuous functions f: R R under the usual addition and multiplication of functions. (You may assume C(R) has all of the properties that make it a ring.) (a) Show C(R) is a commutative ring with 1. (b) Show C (R) is not an integral domain. (Find a zero divisor in C(R) and demonstrate it is in fact a zero divisor.)

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