Inclusion of sets is reversed

An example where X encompasses Y and Y encompasses X, depending on the viewpoint.

• The set of “knowledge shared by A and B” is
• Since it encompasses the set of “knowledge shared by Mr. A, Mr. B, and Mr. C,”
• Shared knowledge f(S) in a set S of persons” means that f(S2) contains f(S1) when S1 contains S2.
• $S_1\subset S_2⟺f(S_1)\supset f(S_2)$
  • This function f has the property of inverting the inclusion relation, but Mr. P and Mr. Q are unaware of the function’s existence.
  • So we call both S and f(S) by the same term, resulting in a disagreement about the inclusion relation

Another case where the inclusion relation of sets is reversed - A wraps around B. - I know both, but the other person only knows one.

• A series of pictures of two people saying different things

concrete example

• “General Knowledge” and “Special Knowledge.”
  • I would think “general” would be broad and almost encompass “special.”
  • Because sometimes “general” is a generalization of “special” that broadens the scope of its coverage.

[https://ja.wikipedia.org/wiki/共変性と反変性_(Computer](https://ja.wikipedia.org/wiki/共変性と反変性_(Computer) Science)

• If A is a superclass of B, then A encompasses B
  • You may assign B to A, but you may not assign A to B.
  • On the other hand, a “function that takes A as an argument” should not be assigned to a “function that takes B as an argument”.
    • Substituting “a function that takes animals in general as arguments” for “a function that takes only cats as arguments” is unsafe, because it might be called with a dog as an argument.
    • So the inclusion relation of the set is inverted.
    • This is called anti-transformation.

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