Tuesday, December 31, 2019

real analysis - Prove that the graph of a continuous function on (infty,infty) is completely determined once one knows a certain countable set of points on it.



A question from Introduction to Analysis by Arthur Mattuck:




Prove that the graph of a continuous function on (,) is completely determined once one knows a certain countable set of points on it.




I have no idea.



Answer



Hint: Q is countable and dense in R.


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