In comparison to math, I think bottom is very close to the idea of an undefined value. What is the value of 4/0? What is the derivative of a step function at 0

In comparison to math, I think bottom is very close to the idea of an undefined value. What is the value of 4/0? What is the derivative of a step function at 0? Mathematics often goes out of its way to make sure things aren't undefined by defining domains that exclude the undefined values. In programming we do the same thing most of the time. I think what I missed is that bottom in Haskell is really an exception. It's a value that doesn't really exist. Trying to force it gives an exception. The real results of a computation are concrete values, non-termination and exceptions.