What would an ill posed math question look like?

I've heard of ill posed problems or inverse problems. is it like working backwards for the solution? I have no idea.What would an ill posed math question look like?
People sometimes mean different things when they say inverse problems, but I think most commonly inverse problems refers to the area of math that attempts to recover parameters of a partial differential equation from information about the solutions to the equation. This is thought of as inverting the map from the space of possible parameters to the set of solutions, and thus the name- inverse problems. An ill posed inverse problem is one where the inverse of this map is either not well-defined, or not continuous in some sense.





The term ill-posed can be used in other contexts as well. It usually means that a map is either not well defined, or not continuous. For example, you can consider the boundary value problem for a given partial differential equation, and the map that takes the boundary data to the solution. This is called ill posed if this map either isn't well defined, or isn't continuous. It wouldn't be well defined if there were two or more possible solutions for one set of boundary data, or if there was some boundary data that didn't give any solution. Failure of continuity is more subtle since you have to define appropriate topologies, but essentially the map might not be continuous if small changes in the boundary data can give rise to arbitrarily large changes in the solution.





The opposite of an ill posed problem is a well posed problem.What would an ill posed math question look like?
lol It could be a math problem that's written poorly, and even math people scratch their heads and wonder what the person is asking. :o)

bourjois