>>11550374>infinitesimally closedude you keep using this as a gotcha, but you have to realize that the construction of the reals is the unique (up to isomorphism) completion of the rationals that follow the Archimedean property - and that property is exactly the statement that 0, the additive identity, is the only infinitesimal in the real field.
So yes, if the difference is infinitesimal, then the difference is 0, meaning they are in fact the same thing.
