Implications

This non-implication, Form 163 \( \not \Rightarrow \) Form 43, whose code is 4, is constructed around a proven non-implication as follows:

  • This non-implication was constructed without the use of this first code 2/1 implication.
  • A proven non-implication whose code is 3. In this case, it's Code 3: 928, Form 163 \( \not \Rightarrow \) Form 78 whose summary information is:
    Hypothesis Statement
    Form 163 <p> Every non-well-orderable set has an infinite, Dedekind finite subset. </p>

    Conclusion Statement
    Form 78 <p> <strong>Urysohn's Lemma:</strong>  If \(A\) and \(B\) are disjoint closed sets in a normal space \(S\), then there is a continuous \(f:S\rightarrow [0,1]\) which is 1 everywhere in \(A\) and 0 everywhere in \(B\). <a href="/articles/Urysohn-1925">Urysohn [1925]</a>, pp 290-292. </p>

  • An (optional) implication of code 1 or code 2 is given. In this case, it's Code 2: 9788, whose string of implications is:
    43 \(\Rightarrow\) 78

The conclusion Form 163 \( \not \Rightarrow \) Form 43 then follows.

Finally, the
List of models where hypothesis is true and the conclusion is false:

Name Statement

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