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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 Summary

Continuity is investigated. The expert proves a continuous interval.

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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 ...

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