# Tagged Questions

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### When does $f_{\omega+1}$ catch up the $G_n$-sequence?

Which is the minimal number k, so that $f_{\omega+1}(n) > G_n$ is true for all $n\ge k$ ? For the definition of $f_{\omega+1}$ look at wikipedia fast growing hierarchy $G_n$ is defined by ...
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For a description look at fast growing hierarchy at wikipedia. $\large f_{\epsilon_0}$ is not defined any more, it is a power tower of omegas, but how many omegas ? I found a defition $$\large ... 1answer 44 views ### Well ordered Set with \le order type Let (x,\le) be well-ordered set and let f: \ x \rightarrow x be monotonically increasing function. Prove that \forall a \in x$$a \le f(a)$$Find an example of set x linearly ... 1answer 56 views ### Functions from ordinals to ordinals I'm trying to solve this problem, which appears in Schimmerling's "A Course in Set Theory." Problem. Find two functions$$f:\omega\rightarrow\omega\cdot2 and ...
Is there a general - and possibly easy! - explicit way to "create" bijective functions between countable ordinals? I mean for example a bijection between $\omega$ and $\omega+\omega$, or a bijection ...