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Results tagged with real-analysis
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user 147246
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
3
votes
3
answers
524
views
Solving interval problems without outer measure
Is it possible to solve the following two problems on intervals using elementary methods, without using the outer measure ?
Problem 1
If $(I_n)$ is a disjoint sequence of subintervals of interval $I$ …
2
votes
Axiomatic construction of trigonometric functions
This answer to Geometrically showing $\frac{\alpha}{\beta} > \frac{\sin\alpha}{\sin\beta}$, for $0 < \beta < \alpha < 90^\circ$ shows using only elementary geometry that $\sin \alpha / \sin \beta < \a …
1
vote
Solving interval problems without outer measure
Further to Nik Weaver's answer, which proves the case of $I$ bounded in Problem 1, the unbounded case is proved below - it follows as a corollary of the bounded case. I will update this answer later i …