I think as long as a sequence of continuous functions converges pointwise to a continuous function on a closed interval, the convergence would be uniform.
Can someone tell me why it's wrong?
2026-04-03 10:11:13.1775211073
Why does the sequence of functions have to be increasing/decreasing in Dini's theorem?
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A typical counterexample is $f_n(x) = \max(1-|nx-1|,0)$, which is a confusing way to say: thin triangles of constant height.