Implications

We have the following indirect implication of form equivalence classes:

140 \(\Rightarrow\) 140
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
140 \(\Rightarrow\) 140

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

Howard-Rubin Number Statement
140:

Let \(\Omega\) be the set of all (undirected) infinite cycles of reals (Graphs whose vertices are real numbers, connected, no loops and each vertex adjacent to  exactly two others). Then there is a function \(f\) on \(\Omega \) such that for all \(s\in\Omega\), \(f(s)\) is a direction along \(s\).

140:

Let \(\Omega\) be the set of all (undirected) infinite cycles of reals (Graphs whose vertices are real numbers, connected, no loops and each vertex adjacent to  exactly two others). Then there is a function \(f\) on \(\Omega \) such that for all \(s\in\Omega\), \(f(s)\) is a direction along \(s\).

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