/sci/ - Science & Math

>>11648325
>Yes my formula does simplify to the same thing
The original one? It doesn't.
[math]2^{|A|^2-|A|} \neq 2^{|A|}[/math]
The brain rot post was the actual brain rot.
>why are you raising 2 to the power of |A|2−|A|?
A reflexive relation [math]R[/math] breaks up into the disjoint [math]R = (R- \Delta) \cup \Delta = R' \cup \Delta[/math].
Then, [math]R' \subseteq [P(A)- \Delta][/math]. Since [math]P(A)- \Delta[/math] has [math]|A|^2-|A|[/math] elements, this gives [math]2^{|A|^2-|A|}[/math] choices of [math]R'[/math], each of which uniquely determines a reflexive relation.