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Results tagged with continued-fractions
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user 172802
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
2
votes
Does using continued fractions work to give a homeomorphism $\mathbb{Q}^+ \rightarrow (\math...
Here is one way to form a (not very) explicit homeomorphism.
As has been mentioned, the function $\phi=(\phi_0,\phi_1)$ from the question applied to the set $I^{>1}$ of irrationals greater than $1$ gi …
- 10.6k