Implications

We have the following indirect implication of form equivalence classes:

137-k \(\Rightarrow\) 0
given by the following sequence of implications, with a reference to its direct proof:

Implication Reference
137-k \(\Rightarrow\) 0

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

Howard-Rubin Number Statement
137-k:

Suppose \(k\in\omega-\{0\}\). If \(f\) is a 1-1 map from \(k\times X\) into \(k\times Y\) then there are partitions \(X = \bigcup_{i \le k} X_{i} \) and \(Y = \bigcup_{i \le k} Y_{i} \) of \(X\) and \(Y\) such that \(f\) maps \(\bigcup_{i \le k} (\{i\} \times  X_{i})\) onto \(\bigcup_{i \le k} (\{i\} \times  Y_{i})\).

0:  \(0 = 0\).

Comment:

Back