you have two envelopes (marked as A and B) on a table, both containing money. the only thing you know is that one of the envelopes contains twice as much money as the other one does. you open the A envelope and there is 100$ in it. now, you have two options: 1) either take the 100$ and go home, or 2) open the another (B) envelope and you get all the money it contains, but not the 100$ that was in A.
now the reasoning could go: there is a 50% chance that B contains 50$, and 50% that B contains 200$. so if I open the B envelope, I can only lose 50$ but win 100$. therefore I should choose the B envelope. yet had he chosen the B envelope at the first place, the exactly same reasoning could still be done. how is that possible?
sorry von, i edited it...
Originally posted by Jusuhgo for B
you have two envelopes (marked as A and B) on a table, both containing money. the only thing you know is that one of the envelopes contains twice as much money as the other one does. you open the A envelope and there is 100$ in it. now, you have two options: 1) either take the 100$ and go home, or 2) open the another (B) envelope and you get all the money it contains, but not the 100$ that was in A.
what would you do and why?
since you have less to lose...
if B has more $$$ then it contains 200 which you gain by 100
if B has less $$$ then it contains 50, which you lose by 50
Originally posted by JusuhHere's a posted discussion:
you have two envelopes (marked as A and B) on a table, both containing money. the only thing you know is that one of the envelopes contains twice as much money as the other one does. you open the A envelope and there is 100$ in it. now, you have two options: 1) either take the 100$ and go home, or 2) open the another (B) envelope and you get all the money it c ...[text shortened]... e exactly same reasoning could still be done. how is that possible?
sorry von, i edited it...
http://mathproblems.info/prob6s.htm
And here's an "exhaustive analysis" of this paradox, referenced in the above article:
www.u.arizona.edu/~chalmers/papers/envelope.html
The analysis describes a method to increase your chances of picking the bigger envelope by using an increasing function and a random number.
russels paradox
Part of the foundation of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction.
Let M be "the set of all sets that do not contain themselves as members". Formally: A is an element of M if and only if A is not an element of A.
Nothing in the system of Frege's Grundgesetze rules out M being a well-defined set. If M contains itself, M is not a member of M according to the definition. If M does not contain itself, then M has to be a member of M, again by the very definition of M. The statements "M is a member of M" and "M is not a member of M" cannot both be true, thus the contradiction (but see Independence from Excluded Middle below).
Originally posted by Ason Pigg2Isn't this a fragment from Wikipedia? You should give credit.
russels paradox
Part of the foundation of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory of Frege leads to a contradiction.
Let M be "the set of all sets that do not contain themselves as members". Formally: A is an element of M if and only if A is not an el ...[text shortened]... both be true, thus the contradiction (but see Independence from Excluded Middle below).
