Is There a Mathematical Formula for Replaceability in Relationships?

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The discussion centers on finding a mathematical formula to express the concept of replaceability in relationships, suggesting that if one person is absent, another equally or more suitable individual would take their place. A proposed formula is shared: "Dian \not\exists u \implies \exists x, x \neq u, |x| \ge |u|," which implies the existence of a replacement. Participants express enthusiasm for the intersection of mathematics and philosophical concepts like metamathematics. The conversation highlights the challenge of quantifying emotional connections and the subjective nature of relationships. Overall, the quest for a mathematical representation of replaceability in relationships remains an intriguing topic.
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I'm looking for a formula to represent the idea that if I didn't have you, someone else would be equally nice or better.

Suggestions?

Thanks,
Dian
 
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\not\exists u \implies \exists x, x \neq u, |x| \ge |u|
Something like that?

Yay for metamathematics :)
 
The standard _A " operator" maps a Null Hypothesis Ho into a decision set { Do not reject:=1 and reject :=0}. In this sense ( HA)_A , makes no sense. Since H0, HA aren't exhaustive, can we find an alternative operator, _A' , so that ( H_A)_A' makes sense? Isn't Pearson Neyman related to this? Hope I'm making sense. Edit: I was motivated by a superficial similarity of the idea with double transposition of matrices M, with ## (M^{T})^{T}=M##, and just wanted to see if it made sense to talk...

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