![MathType on Twitter: "When studying function sequences, pointwise convergence is not enough to ensure that sequences of continuous functions have a continuous limit. Uniform convergence is necessary to maintain this basic property, MathType on Twitter: "When studying function sequences, pointwise convergence is not enough to ensure that sequences of continuous functions have a continuous limit. Uniform convergence is necessary to maintain this basic property,](https://pbs.twimg.com/media/D0QrGURWsAAsarV.jpg:large)
MathType on Twitter: "When studying function sequences, pointwise convergence is not enough to ensure that sequences of continuous functions have a continuous limit. Uniform convergence is necessary to maintain this basic property,
![SOLVED: 1 (This is essentially Exercise 24.2) Let fn() = # 1 mark) Find the pointwise limit f (x) of fn(x) on R (b) (2 marks) Prove that fn - f uniformly SOLVED: 1 (This is essentially Exercise 24.2) Let fn() = # 1 mark) Find the pointwise limit f (x) of fn(x) on R (b) (2 marks) Prove that fn - f uniformly](https://cdn.numerade.com/ask_images/c292ce51c9004667a7f198d156a775a7.jpg)
SOLVED: 1 (This is essentially Exercise 24.2) Let fn() = # 1 mark) Find the pointwise limit f (x) of fn(x) on R (b) (2 marks) Prove that fn - f uniformly
![real analysis - Question about proof: Uniform cauchy $\Rightarrow$ Uniform convergence - Mathematics Stack Exchange real analysis - Question about proof: Uniform cauchy $\Rightarrow$ Uniform convergence - Mathematics Stack Exchange](https://i.stack.imgur.com/ruUCQ.png)
real analysis - Question about proof: Uniform cauchy $\Rightarrow$ Uniform convergence - Mathematics Stack Exchange
![On the Uniform Convergence of Fourier Series - Morgan - 1936 - Journal of the London Mathematical Society - Wiley Online Library On the Uniform Convergence of Fourier Series - Morgan - 1936 - Journal of the London Mathematical Society - Wiley Online Library](https://londmathsoc.onlinelibrary.wiley.com/cms/asset/b5397094-885d-467e-9b9b-b25180bf8007/jlms_s1-11.3.162.fp.png)