True or False? Continuity Problem: f(0)=g(0)

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SUMMARY

The discussion centers on the continuity problem regarding the functions f and g at the point 0, specifically whether f(0) equals g(0) given their continuity and the condition f(1/(2n+7))=g(1/(7-2n)) for all positive integers n. The consensus leans towards the conclusion that the statement is false, as the limit behavior of the sequences defined by the functions does not guarantee equality at the point of continuity. The relevant equations lim x->0 f(x)=f(0) and lim x->0 g(x)=g(0) are crucial to understanding the implications of continuity in this context.

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mathmajor2013
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1. Homework Statement

True or false? If f and g are continuous at 0 and f(1/(2n+7))=g(1/(7-2n)) for all positive integers n, then f(0)=g(0).

2. Homework Equations

lim x->0 f(x)=f(0)
lim x->0 g(x)=g(0)

3. The Attempt at a Solution

NO CLUE. My intuition says false.
 
Physics news on Phys.org
What is the definition of continuity at 0?

What happens as n--> infinity?
 

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