We have the following indirect implication of form equivalence classes:
Implication | Reference |
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305 \(\Rightarrow\) 306 |
Cardinality of the set of Vitali equivalence classes, Kanovei, V.G. 1991, Mat. Zametki |
Here are the links and statements of the form equivalence classes referenced above:
Howard-Rubin Number | Statement |
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305: | There are \(2^{\aleph_0}\) Vitali equivalence classes. (Vitali equivalence classes are equivalence classes of the real numbers under the relation \(x\equiv y\leftrightarrow(\exists q\in{\Bbb Q})(x-y=q)\).). \ac{Kanovei} \cite{1991}. |
306: | The set of Vitali equivalence classes is linearly orderable. (Vitali equivalence classes are equivalence classes of the real numbers under the relation \(x\equiv y\leftrightarrow (\exists q\in{\Bbb Q})(x-y = q)\).). |
Comment: