5. For n E N, let fn:X → R such that o # X c R. If each fn is continuous on X but f:X → R is not, then fn does not converge pointwise to f.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Identify if the following statement is true or false. If the statement is true, then prove. Otherwise, if the statement is false, then give a counterexample. (Note: short and precise proofs only, no need for lengthy ones with so many explanations)

5. For n E N, let fn:X → R such that o + X c R. If each fn is continuous on X but f:X → R is not, then
fn does not converge pointwise to f.
Transcribed Image Text:5. For n E N, let fn:X → R such that o + X c R. If each fn is continuous on X but f:X → R is not, then fn does not converge pointwise to f.
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