/sci/ - Science & Math

guys I've proven that absense of evidence is evidence of absence.
what should I so with this discovery?

the only assumption necessary for this proof is that none of the events have a probability of 0 of occuring.
let x be some event and e be an event which makes x more likely when e is true , aka evidence for x so P(x|e)>P(x) and let x' and e' be the complements/negation of x and e and let <=> denote a 2 way implication, in other words "if and only if"
then P(x|e)>P(x) <=> 1-P(x|e)<1-P(x) <=> P(x'|e) <P(x') call this result (1.)
then start again with P(x|e)>P(x) <=> by bayes theorem P(e|x)P(x)/P(e) > P(x) <=> P(e|x) > P(e) now apply result (1.) <=> P(e'|x) < P(e') <=> by bayes theorem P(x|e')P(e')/P(x) < P(e') <=> P(x|e') < P(x) <=> applying result 1 again P(x'|e') > P(x')
Q.E.D.

So e being evidence for x is equivalent to not e being evidence for not x.
And before you complain that absence does not mean negation, look at the original phrase
>absence of evidence is not evidence of absence
here evidence of absence clearly means the absence of something, meaning there is no such thing, meaning the thing does not exist, meaning more generally that the event is not true i.e. the negation of the event. therefore rigorously speaking, absence does mean negation.