Gw mau tau Perbandingan dengan definisi infinitesimal dari Definisi limit (ε, δ)

Keisler proved that a hyperreal definition of limit reduces the logical quantifier complexity by two quantifiers. Namely,  converges to a limit L as  tends to a if and only if the value  is infinitely close to L for every infinitesimal e. (See Microcontinuity for a related definition of continuity, essentially due to Cauchy.)

Infinitesimal calculus textbooks based on Robinson's approach provide definitions of continuity, derivative, and integral at standard points in terms of infinitesimals. Once notions such as continuity have been thoroughly explained via the approach using microcontinuity, the epsilon–delta approach is presented as well. Karel Hrbáček argues that the definitions of continuity, derivative, and integration in Robinson-style non-standard analysis must be grounded in the ε–δ method, in order to cover also non-standard values of the input. Błaszczyk et al. argue that microcontinuity is useful in developing a transparent definition of uniform continuity, and characterize the criticism by Hrbáček as a "dubious lament". Hrbáček proposes an alternative non-standard analysis, which (unlike Robinson's) has many "levels" of infinitesimals, so that limits at one level can be defined in terms of infinitesimals at the next level.