Changes

==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.

: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,y,z \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> Then suppose: #<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> Then <math>T = \{\emptyset\}</math> Q.E.D. ===The Pitt-122Depp Addendum=== Adding the constraint that 'everybody loves somebody', or equivalently that: :<math>\forall i \in H \quad \exists h \in H \;\mbox{s.t.252512&spn=0}\; h \succ_i \{\emptyset\}</math> does not make rational preferences sufficient to guarantee that <math> T \ne \{\emptyset\}</math>.011501 '''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>#<math>j \succ_i h \quad \forall h\ne j \in H\quad\mbox{(Brad loves Johnny)}</math>#<math>\exists h' \ne i,0j \; \mbox{s.015535&t.}\; h'\succ_j h \quad \forall h\ne h',i \in H\quad\mbox{(Johnny loves his wife)}</math> Then <math>T =m&z=16&vpsrc=6 map\{\emptyset\}</math> Q.E.D. Note: Objections to this proof on the grounds of the inclusion of Johnny Depp should be addressed to [https://scholar.harvard.edu/rabin/capital-montana Matthew Rabin]. Additional Note: The claim that [https://en.wikipedia.org/wiki/Depp_v._Heard Johnny loves his wife hasn't aged well]. This should be changed to Johnny loves [https://en.wikipedia.org/wiki/Vanessa_Paradis French Actress and Singer Vanessa Paradis]) at your earliest convenience, his longest romantic partner and mother to his two children, as the odds of him doing better are now approaching zero.

==Future AvailabilityThe Age Rule==

Let where <math>H\underline{Age} = 18 \;\mbox{if}\; Age_j \ge 18</math> denote the set of all entities, perhaps Humans, though we might also include dogs, cats and horses, according to historical precedentexcept in Utah.

Let <math>T<I finally found a source to attribute this to: XKCD predates my posting significantly with its [http://xkcd.com/math> denote the set of pairs of individuals who have True 314/ 'Standard Creepiness Rule']. ==Random Love, such that:==

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].