How does a computer know if it has compact domains? Or we can only do it manually?
dchen1
In theory we should have coercivity, but in practice, shouldn't our x usually be within a certain range anyways? So we can just hard code that range. Or I would imagine even in terms of e^-x, if we are using floating point then we will just stop on positive infinity once we get large enough, then can't our program just tell us that the answer is outside the range that we can represent with floating point?
keenan
Yinz are thinking too much about the behavior of the computer, and not enough about whether the problem you're trying to solve is meaningful in the first place. :-)
Basically if you have an objective that is not coercive, there should be alarm bells going off telling you, "the problem you think you want to solve is not the one you want to solve!" Because it does not have a meaningful solution.
Relying on the computer to tell you whether the problem is meaningful or not is a dangerous game (especially when dealing with the dark art of floating point).
How does a computer know if it has compact domains? Or we can only do it manually?
In theory we should have coercivity, but in practice, shouldn't our x usually be within a certain range anyways? So we can just hard code that range. Or I would imagine even in terms of e^-x, if we are using floating point then we will just stop on positive infinity once we get large enough, then can't our program just tell us that the answer is outside the range that we can represent with floating point?
Yinz are thinking too much about the behavior of the computer, and not enough about whether the problem you're trying to solve is meaningful in the first place. :-)
Basically if you have an objective that is not coercive, there should be alarm bells going off telling you, "the problem you think you want to solve is not the one you want to solve!" Because it does not have a meaningful solution.
Relying on the computer to tell you whether the problem is meaningful or not is a dangerous game (especially when dealing with the dark art of floating point).