How to Prove a Set of Functions is Closed Under Addition (Example with functions s.t. f(0) = 0)

SOLVED: Problem 1.1. Let (R,t) be field and F(R) the set of all functions f : R+ R. Prove that (F(R) +, is commutative ring with unity, with the addition and multiplication

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Solved 1. Determine if the set S = {f:f is a real valued

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Show the Set of Functions such that f(0) = 1 is Not Closed Under Addition

Show the Set of Functions such that f(0) = 1 is Not Closed Under Addition

Let G be the set of all continuous functions with

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