Infinite tetration and superroot of infinitesimal

[Ivars]

If you want to treat the infinitesimal as always positive, then it's simply the logical end of the sequence dx, dx^2, dx^3, ..., dx^(1/dx). In ordinal notation, it's 1/(omega^omega), and omega^omega is a rather small ordinal in the hierarchy of countable infinities. (Not that I particularly like the hierarchy.)

(1/dx) is bigger than any n. It lies outside sequence of infinite natural numbers. (please look into non-standard analysis). It is a qualitatively different number. And after 1/dx, we still have infinite INTEGERS. What are they?