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    Continuity Proofs of Functions

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    1. Prove that any function f: Natural Nos. --> R is continuous (N --> R).
    2. Prove that if a function f: I --> R is continuous and I is an interval then the image f(I) is an interval.

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    Solution Preview

    1. Since every subset of natural numbers is open in natural numbers, inverse image of an open set in R is open in natural numbers. Hence any function f mapped from natural numbers to R is ...

    Solution Summary

    Continuity is investigated. The expert proves a continuous interval.