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Results tagged with continuity
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user 172802
10
votes
Accepted
For this continuous non differentiable function $f$ How to determine $\sup\{a\}$ s.t $\lim\l...
I leave my proof below, although as user479223 mentions, this is the same as showing Hölder continuity of the Weierstrass function, which is well known (see this MSE answer). …
- 10.6k
33
votes
Accepted
What is the smallest set of real continuous functions generating all rational numbers by ite...
It is enough with one continuous function. First, I'll give a simple example with one function which is discontinuous at one point. To do it, consider the function $$f:(0,\pi+1)\to(0,\pi+1)$$ with
$$
…
- 10.6k