You can check the answer with a calculator of course. The largest is e^pi.
judy - 10 years ago
3^2 >2^3 so I voted pi^e.
Paul - 10 years ago
Thanks for taking part, Marty.
Marty - 10 years ago
My comment got garbled on submission. I don't know why.
Marty - 10 years ago
We are comparing x ^ y with y ^ x.
For example, 2 ^ 3 4 ^ 3 (that is, 81 > 64) and 2 ^ 100 is WAY bigger than 100 ^ 2.
As the values of x and y increase, the significance of the exponent dominates more and more.
So I voted for the choice with the higher exponent (that is, e ^ pi seems likely to be the greater result).
Paul - 10 years ago
This poll is about people's intuition, Vasile. I want people to vote BEFORE embarking on a proof. Thanks for your interest.
Vasile - 10 years ago
The problem is quite simple. In Romania any reasonable high school student from year 11 would be able to tell the answer. You don't have to cast a vote when there is an elementary proof in hand.
Thanks Judy also.
You can check the answer with a calculator of course. The largest is e^pi.
3^2 >2^3 so I voted pi^e.
Thanks for taking part, Marty.
My comment got garbled on submission. I don't know why.
We are comparing x ^ y with y ^ x.
For example, 2 ^ 3 4 ^ 3 (that is, 81 > 64) and 2 ^ 100 is WAY bigger than 100 ^ 2.
As the values of x and y increase, the significance of the exponent dominates more and more.
So I voted for the choice with the higher exponent (that is, e ^ pi seems likely to be the greater result).
This poll is about people's intuition, Vasile. I want people to vote BEFORE embarking on a proof. Thanks for your interest.
The problem is quite simple. In Romania any reasonable high school student from year 11 would be able to tell the answer. You don't have to cast a vote when there is an elementary proof in hand.