Quote: “Topological fixed points are non constructive.”
Yeah. This fact is kind of crazy, I still haven’t made my peace with it. For example, there’s a computable continuous function from the unit square to itself without any computable fixed points.
I think that’s kinda cheating, because you are only approximating the outputs anyways (since they are real numbers), and regardless “the real numbers are a monstrosity” is something I’ve learned.
Perhaps you can come up with a non monstrous example?
Quote: “Topological fixed points are non constructive.”
Yeah. This fact is kind of crazy, I still haven’t made my peace with it. For example, there’s a computable continuous function from the unit square to itself without any computable fixed points.
I think that’s kinda cheating, because you are only approximating the outputs anyways (since they are real numbers), and regardless “the real numbers are a monstrosity” is something I’ve learned.
Perhaps you can come up with a non monstrous example?