I think the goal posts are moved here though, the first equation is algebraic (and b is implicitly some element of a semigroup at least?) while the second is asking something about limits?
As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
I think the goal posts are moved here though, the first equation is algebraic (and b is implicitly some element of a semigroup at least?) while the second is asking something about limits?
a and b are numbers. In the example a=0 while b=sin(1/0).
We could consider a linear function space and a functional where we evaluate at x=0, but then sin(1/x) is not an element or the functional is not defined for all elements of the space. Domains matter for questions like this.
As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.