(professor hints)
A Road Map to Glory
- Write Down the negation of the definition of an accumulation point.
- Prove that there exists a positive real number δ for which (x0−δ,x0+δ)∩D={x0}
- Prove that the only number x satisfying x∈D and |x−x0|<δ is x=x0.
- Prove that for such an x, |f(x)−f(x0)|<ϵ for every positive number ϵ
I have trouble starting from the second bullet point. After that I wouldn't know how to connect it with the third. I wanted to ask for help regarding these two bullets. I understand that due to the negation of accumulation point there exists a finite neighborhood of x0.Im not sure how this connects to the third bullet. I understand that it the δ-neighborhood of x0, however how is that neighborhood finite.
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