Implications

We have the following indirect implication of form equivalence classes:

4 \(\Rightarrow\) 4
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
4 \(\Rightarrow\) 4 On Cardinal Numbers, Whitehead, A.N. 1902, Amer. J. Math.

Here are the links and statements of the form equivalence classes referenced above:

Howard-Rubin Number Statement
4:

Every infinite set is the union of some disjoint family of denumerable subsets. (Denumerable means \(\cong \aleph_0\).)

4:

Every infinite set is the union of some disjoint family of denumerable subsets. (Denumerable means \(\cong \aleph_0\).)

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