Implications

This non-implication, Form 163 \( \not \Rightarrow \) Form 407, 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: 3927, whose string of implications is:
    407 \(\Rightarrow\) 43 \(\Rightarrow\) 78

The conclusion Form 163 \( \not \Rightarrow \) Form 407 then follows.

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

Name Statement

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