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Results tagged with real-analysis
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user 12978
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
7
votes
Accepted
reverse mathematics strength of "Lipschitz functions are somewhere differentiable"
(Update: I made my answer clearer and also fixed the references and added more.)
Your theorem should be true in every $\omega$-model of $\mathsf{RCA}_0$ as follows. The following paper
Brattka, Mil …
- 6,287
50
votes
Two (probably) equal real numbers which are not proved to be equal?
Thomson’s problem for $n = 7$ provides a nice example:
$$\min_{x_1, \ldots, x_7 \in \mathbb{S}^2} \sum_{i=1}^7 \sum_{j = i + 1}^7 \frac{1}{|x_i - x_j|} = \frac{1}{2} + 10 \frac{1}{\sqrt{2}} + 5\sqrt{ …
4
votes
floating point representation via the perspective of TTE/computable analysis
Background:
For those who don't know, TTE is two things: A type-two Turing machine a theoretical model of computation whose input and output is an infinite sequence of natural numbers. (Such a machin …
- 6,287
6
votes
Accepted
Recent trends in effective analysis
(At François's request, my comment in now an answer.)
Yes, it is still an active research area. It however is spread out throughout a number of camps (traditions): The Weihrauch camp, the reverse mat …
- 6,287