Please provide details on how to solve it. Thanks The purpose of this project is

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Please provide details on how to solve it. Thanks

The purpose of this project is to ascertain under what conditions an additive function has a limit at each point in R. We say that f : R rightarrow R is additive if for all x, y R, f(x + y) = f(x) + f(y). In what follows, f is an additive function. Prove that if there are M > 0 and a > 0 such that if x [-a, a], then |f(x)| le M, then f has a limit at each x in R and Prove that if f has a limit at each x R, then there are M > 0 and a > 0 such that if x [-a, a], then |f(x)| le M. You have now proven that f:R rightarrow R is additive, then f has a limit at each point in R iff there are M > 0 and a > 0 such that if x [-a, a], then |f(x)| ge M. In addition, if the condition is satisfied, .

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Please check this link .I written solution

https://docs.google.com/file/d/0B2nSGCdeENaIenJoM2E2ME1LOGM/edit?usp=sharing

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