Farmageddon said:
|
Standard and non-standard calculus are equivalent in term of power. Some theorems are easier to prove in standard form, other are easier in non-standard; also, some people seem to like the more hands-on approach to infintesimal quantities that the non-standard calculus permits. In which you have the standard part as a "static" concept instead of the "limit" that is a sort of dynamic one - again, just preferences.
Digression:
In my experiences physicists already work with non-standard calculus in their head all the time, and they talk to each other in terms of dividing and multplying by infinitesimal quantities routinely. Non-standard calculus is just the clean formalization of that intuitive behaviour, no matter how many times your standard calculus teacher will try to hammer in your head that Integral(f(x)dx) is just a symbol and not the sum of products of f(x) by an infinitesimal quantity.
Digression over, anyway :)
You can work with limits or you can take the standard part of an R* number, and you get to the very same result ( I think that's called Leibnitz equivalence, actually ). But not even in non-standard calculus division by zero is contemplated, merely the division by an infinitesimal. So my point was that solving that equation (it has a solution in R*) is really a different issue from division by zero.
