Zeration

[JmsNxn]

You are confusing your systems of logic. Yes, in hyperreals \(e^{-\infty}\) is infinitesimal. But in the extended reals it is 0. It depends on how we interpret these equations. And as we are operating under traditional limits, and not hyperreal limits--the result stands.

If e^-∞ = 0, then e^-(-∞) = 1/e^-∞ = 1/0. But you can not divide by zero.

Nahhhh, none of that is how things work. The function \(\exp(x) : (-\infty,0] \to (0,1]\), which the limit on the boundary as \(x \to -\infty\), tends to the limit on the boundary of codomain. Which is zero. Same principle here.