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 ...
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 ...
In ZFC there seem to be two ways to define a function, as an ordered triple of domain, codomain and the set of ordered pairs that make its graph, or a relation over the two sets. Whichever we use ...