Why we need so called uniform convergence

Why we need so called uniform convergence
in this video
we talk many examples about why we need uniform convergence

Advanced mathematics list:

Group representation for finite group
https://www.youtube.com/playlist?list=PLg9w7tItBlZvxk4eus_gi2Wp3yYAEXF9-

exact sequences
https://www.youtube.com/playlist?list=PLg9w7tItBlZuI7n7notRRA2jol69e9mc9

Ring theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtfPKHWGlU55kqafEgUu45u

group theory lecture
https://www.youtube.com/playlist?list=PLg9w7tItBlZtSHrTTVjEzAsUcO69YXY7v

Category theory
https://www.youtube.com/playlist?app=desktop&list=PLg9w7tItBlZtI1njDjtXt_0Hkqbn9RVvi

Field theory in abstract algebra
https://www.youtube.com/playlist?list=PLg9w7tItBlZtA6XhMIgIPkgj_SDKChbN-

Mathematical analysis
https://www.youtube.com/playlist?list=PLg9w7tItBlZu-yFYxQrWrFKcdOHRz2Fkh

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