Implications

We have the following indirect implication of form equivalence classes:

4 \(\Rightarrow\) 75
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
4 \(\Rightarrow\) 405 clear
405 \(\Rightarrow\) 75 clear

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 \(\cong \aleph_0\).)

405:

Every infinite set can be partitioned into sets each of which is countable and has at least two elements.

75:

If a set has at least two elements, then it can be partitioned into well orderable subsets, each of which has at least two elements.

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