Answered: Let (X, d) be a metric space, f,g:X → R…

Let (X, d) be a metric space, f,g:X → R some functions and xo E X, q E R. Assume that f(x) = g(x) whenever x E Bf (xo). Prove that if f (x) → q as x → Xo, then g(x) → q as x → Xo.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.2: Mappings

Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

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Let (X, d) be a metric space, f,g:X → R some functions and xo E X, q E R. Assume that
f(x) = g(x) whenever x e Bf (xo).
Prove that if f (x) → q as x → xo, then g(x) → q as x → Xo.

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