Statement:
Every Dedekind finite subset of \({\Bbb R}\) is finite.
Howard_Rubin_Number: 13
Parameter(s): This form does not depend on parameters
This form's transferability is: Transferable
This form's negation transferability is: Negation Transferable
Article Citations:
Book references
Zermelo's Axiom of Choice, Moore, G.H., 1982
Note connections:
Note 94
Relationships between the different definitions of finite
| Howard-Rubin Number | Statement | References |
|---|---|---|
| 13 A | \({\Bbb R}\) has no dense Dedekind finite subset. \ac{Brunner} \cite{1982d} and note 94. |
|
| 13 B | There is a separable topological space \(X\) and a set \(A\subseteq{\Bbb R}\) such that \(X^{A\times\omega }\) has no dense, Dedekind finite subset. \ac{Brunner} \cite{1982d} and note 94. |
|
| 13 C | Strong Bolzano-Weierstrass Theorem: In \({\Bbb R}\) for every bounded, infinite set \(A\), there is a convergent, injective sequence whose terms are in \(A\). \ac{Herrlich/Strecker} \cite{1997}. \iput{Bolzano-Weierstrass theorem} |
|