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That said, if you genuinely believe:==Definition of True Love==
:Let <math>p\leftH</math> denote the set of all entities (You \cap The\perhaps Humans,One \ne \{\empty\}\though we might also include dogs,|\cats and horses,First\,Glance\rightaccording to historical precedent) \gg 0</math>.
then please stop by my office 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) \wedge (F533j \succ_i h \quad \forall h \ne j) at , \quad h \in H \cup \{\emptyset\}</math> Note that:*The definition employs strict preferences. A polyamorous definition might allow weak preferences instead.*The union with the Haas School of Business empty set allows for people who would rather be alone ([http:e.g. Liz Lemon/Tina Fey), provided that we allow a mild abuse of notation so that <math>\{\emptyset\} \succ_{i} h</mapsmath>.google.com ==The Existence of True Love== Can we prove that <math> T \ne \{\emptyset\}</mapsmath> ?msid ===The Brad Pitt Problem=218233511539606995594.0004adfa2636c2d290827&msa=0&ll=37 Rational preferences aren't sufficient to guarantee that <math> T \ne \{\emptyset\}</math>.872008 '''Proof:''' Recall that a preference relation is rational if it is complete and transitive:#Completeness: <math>\forall x,y \in X: \quad x \succsim y \;\lor\; y \succsim x</math>#Transitivity: <math>\forall x,-122.252512&spn=0.011501y,0.015535&t=m&z=16&vpsrc=6 map]) at your earliest convenience.\in X: \quad \mbox{if}\; \; x \succsim y \;\wedge\; y \succsim 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 \;\wedge\; y \not{\succsim} x</math>
==Future Availability==Then suppose:
Please check back for updates.#<math>\forall j \ne i \in H \quad i \succ_j h \quad \forall h\ne i \in H\quad\mbox{(Everyone loves Brad)}</math>#<math>\{\emptyset\} \succ_i h \quad \forall h \in H\quad\mbox{(Brad would rather be alone)}</math>
Let <math>H</math> denote Adding the set of all entitiesconstraint that 'everybody loves somebody', perhaps Humans, though we might also include dogs, cats and horses, according to historical precedent.or equivalently that:
Let :<math>\forall i \in H \quad \exists h \in H \;\mbox{s.t. }\; h \succ_i \{\emptyset\}</math> does not make rational preferences sufficient to guarantee that <math>T\ne \{\emptyset\}</math>. '''Proof''': Suppose:#<math>\forall k \ne i,j \in H \quad i \succ_j h \quad \forall h\ne i,k \in H\quad\mbox{(Everyone, except Johnny, loves Brad)}</math> denote #<math>j \succ_i h \quad \forall h\ne j \in H\quad\mbox{(Brad loves Johnny)}</math>#<math>\exists h' \ne i,j \; \mbox{s.t.}\; h'\succ_j h \quad \forall h\ne h',i \in H\quad\mbox{(Johnny loves his wife)}</math> Then <math>T = \{\emptyset\}</math> Q.E.D. Note: Objections to this proof on the set grounds of pairs the inclusion of individuals who have True Love, Johnny Depp should be addressed to [https://scholar.harvard.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==
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==
Ioriginally tried to write an [[economic definition of true love]] for Valentine'm afraid that s Day in 2009 on a page entitled "Dating Ed is '''currently unavailable''' for dating at this time". Exceptions to this can be made if you have a Math(s) PhIt became one of the most popular pages on my website, receiving hundreds of thousands of views, and I maintained it across several different wikis.DThe version below no longer includes information about dating me, as I'm now married, but does bring back some other material that was deleted over the years.
Then <math>T ==True Love==\{\emptyset\}</math> Q.E.D.
===DefinitionThe Pitt-Depp Addendum===
An amusing exploration of Random Love was recently posted as [http:<math>\forall\{i,j\} \in T: \quad (i \succ_j h \forall h \ne i) \and (j \succ_i h \forall h \ne j), \; h \in H \cap \{\emptyset\}</math>/what-if.xkcd.com/9/ XKCD Blog article No. 9].
