Tagged Questions
3
votes
1answer
77 views
(Non) equivalence of regular cardinal definitions
The usual definition of a regular cardinal is "$\kappa$ is regular if $cf(\kappa) = \kappa$", which, assuming the axiom of choice, is equivalent to this definition: "$\kappa$ is regular iff it cannot ...
0
votes
2answers
47 views
Question about power of sets
If two sets are finite and they have the same power, can we say that the two sets are equivalent?
Is every finite set countable?
1
vote
2answers
64 views
Number of Vertices of Graphs
So, I was looking at some graph theoretical stuff, more specifically Topological Graph Theory, and I had a question about the definition of graphs: is there usually a condition in the definition ...
0
votes
2answers
134 views
Definition of denumerable (countable) set
When we say that a set $S$ is denumerable, that is, there is a bijection $S \to \omega$, do we mean that there exists such a bijection or do we mean that we have one and are talking about a pair ...
2
votes
4answers
165 views
What's the definition of $\omega$?
This is a follow up on a comment to one of my previous questions. What's the definition of $\omega$?
Are the following equivalent definition of $\omega$:
$\omega$ is the initial ordinal of ...
3
votes
3answers
195 views
What does $H(\kappa)$ mean?
As the typical references (Wikipedia, Mathworld, etc.) don't seem to address this satisfactorily, I figured this would be a good place to put a nice formal definition. Hence:
I've heard that if ...
