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Based on what I have read so far, to me it sounds like Alan Turing's solution the Entscheidungsproblem means that there is no algorithmic solution to tell whether a given algorithm with input will eventually halt or not. But why is this so crucial in the "computability" world?
It sounds like if I write a program (let's call it P) and have an input, there doesn't exist a separate program that can read in P and the input to tell whether P will halt or not - so what? Can't I just run P to see if it will halt?
I would greatly appreciate it if someone can explain to me what it means to have no algorithm to decide whether a program will halt or not.