Here’s a math problem that came up while I was cleaning up some decision theory math. Oh mighty LW, please solve this for me. If you fail me, I’ll try MathOverflow :-)
Prove or disprove that for any real number p between 0 and 1, there exist finite or infinite sequences x_m and y_n of positive real numbers, and a finite or infinite matrix of numbers varphi_{mn} each of which is either 0 or 1, such that:
ETA Now I also know that finite sequences can only yield rational p. It was quite fun to prove.
ETA 2 Asked it on MathOverflow several hours ago, no good answers yet.
ETA 3 Gerald Edgar on MathOverflow has solved it. This is the third math problem I posted to MO, each one had stumped me for more than a day, and each one was solved in less than a day.
Here’s a math problem that came up while I was cleaning up some decision theory math. Oh mighty LW, please solve this for me. If you fail me, I’ll try MathOverflow :-)
Prove or disprove that for any real number p between 0 and 1, there exist finite or infinite sequences x_m and y_n of positive real numbers, and a finite or infinite matrix of numbers varphi_{mn} each of which is either 0 or 1, such that:
1 \sum%20x_m=1%0A\\2)\sum%20y_n=1%0A\\3)\forall%20n\sum%20x_m\varphi_{mn}=p%0A\\4)\forall%20m\sum%20y_n\varphi_{mn}=p)
Right now I only know it’s true for rational p.
ETA Now I also know that finite sequences can only yield rational p. It was quite fun to prove.
ETA 2 Asked it on MathOverflow several hours ago, no good answers yet.
ETA 3 Gerald Edgar on MathOverflow has solved it. This is the third math problem I posted to MO, each one had stumped me for more than a day, and each one was solved in less than a day.