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Denoting EdI originally tried to write an [[economic definition of true love]] for Valentine's availability <math>A</math> at time <math>t</math> as <math>A_t</math>Day in 2009 on a page entitled "Dating Ed". It became one of the most popular pages on my website, receiving hundreds of thousands of views,and defining <math>T</math> I maintained it across several different wikis. The version below no longer includes information about dating me, as belowI'm now married, it appears but does bring back some other material that:was deleted over the years.
:<math>\forall t \in \{now, \ldots, \infty\} \;\;A_t=0</math> because :<math>\{LB,EE\} \in T\; </math> (see below) ==Definition of True Love== ===Definition===
===The Existence of True Love===
====The Brad Pitt Problem====
====The Pitt-Depp Addendum====
Economic definition of true love (view source)
Revision as of 20:00, 18 December 2020
, 20:00, 18 December 2020→The Pitt-Depp Addendum
==Current AvailabilityPreamble==
Let <math>H</math> denote the set of all entities (perhaps Humans, though we might also include dogs, cats and horses, according to historical precedent).
Let <math>T</math> denote the set of pairs of individuals who have True Love, such that:
:<math>\forall\{i,j\} \in T: \quad (i \succ_j h \quad \forall h \ne i) \and wedge (j \succ_i h \quad \forall h \ne j), \quad h \in H \cap cup \{\emptyset\}</math>
Note that:
*The union with the empty set allows for people who would rather be alone (e.g. Liz Lemon/Tina Fey), provided that we allow a mild abuse of notation so that <math>\{\emptyset\} \succ_{i} h</math>.
Can we prove that <math> T \ne \{\emptyset\}</math> ?
Rational preferences aren't sufficient to guarantee that <math> T \ne \{\emptyset\}</math>.
Recall that a preference relation is rational if it is complete and transitive:
#Completeness: <math>\forall x,y \in X: \quad x \succsim y \;\orlor\; y \succsim x</math>#Transitivity: <math>\forall x,y,z \in X: \quad \mbox{if}\; \; x \succsim y \;\andwedge\; y \succsim x z \;\mbox{then}\; x \succsim z</math>
Also recall the definition of the strict preference relation:
:<math>x \succ y \quad \Leftrightarrow \quad x \succsim y \;\andwedge\; y \not{\succsim} x</math>
Then suppose:
Then <math>T = \{\emptyset\}</math> Q.E.D.
Adding the constraint that 'everybody loves somebody', or equivalently that:
Then <math>T = \{\emptyset\}</math> Q.E.D.
Note: Objections to this proof on the grounds of the inclusion of Johnny Depp should be addressed to [httphttps://elsascholar.berkeleyharvard.edu/~rabin/ capital-montana Matthew Rabin]. ==The Age Rule== The defacto standard age rule is as follows: Denote two people <math>i\;</math> and <math>j\;</math> such that <math>Age_i \le Age_j</math>, then it is acceptable for them to date if and only if :<math>Age_i \ge \max \left\{\left(\frac{Age_j}{2}\right)+7\;,\;\underline{Age}\right\}</math> where <math>\underline{Age} = 18 \;\mbox{if}\; Age_j \ge 18</math>, except in Utah. I finally found a source to attribute this to: XKCD predates my posting significantly with its [http://xkcd.com/314/ 'Standard Creepiness Rule']. ==Random Love== An amusing exploration of Random Love was recently posted as [http://what-if.xkcd.com/9/ XKCD Blog article No. 9].
