>>105
Infinitesimals are merely heuristics for the asymptotic boundary conditions of a non-halting recursive process (Archimedes'
Method of indivisibles), which can be distilled via the transfer principle.
http://en.wikipedia.org/wiki/Transfer_principle
http://en.wikipedia.org/wiki/The_Method_of_Mechanical_Theorems
>>106
That doesn't mean infinity can't be treated as an useful concept in mathematics, though.
It hides the complexity of thinking about non-halting recursive processes sure, and gives you a declarative syntax. But the problem is that this syntax has become so entrenched within mathematics that people believe the semantics of infinity is the same thing as the syntax, and that therefore infinity itself must exist in an absolute declarative sense.
People have confused the map for the territory.