What exactly is the halting problem?

Question

Whenever people ask about the halting problem as it pertains to programming, people respond with \"If you just add one loop, you\'ve got the halting program and therefore yo

Answer 1

Yet another example. I recently ran into something called hailstone numbers. These numbers form a sequence with these rules

f(n) is odd  -  f(n+1) = 3*f(n)+1
f(n) is even -  f(n+1) = f(n)/2

Currently, it is assumed that all starting points will eventually arrive at 1, and then repeat 4,2,1,4,2,1,4,2,1... However there is no proof for this. So right now the only way to determine if a number terminates when fed into the hailstone sequence is to actually compute it until you arrive at 1.

This is the key to how I understand the halting problem. How I understand it is that you cannot for sure know a that a program will/will not halt unless you actually run the program. So any program that you write that could give you an answer for sure to the halting problem, would have to actually run the program.