An intuition is that an inverse of an infinite quantity is an infinitesimal, but can there be other approaches?
2026-03-28 13:42:05.1774705325
Can there be a field or integral domain with infinitely large quantities but without infinitesimals?
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Consider $\mathbb{Z}[x]$. It is an intergral domain and you can put an ordering on it so that $x$ is bigger than any integer.
Fields won't work if you want an ordering compatible with field operations so you would need to think of a different notion of big. Maybe some comparison to the characteristic field? Maybe the size of an element is the degree of the polynomial which it solves with transendentals being infinitely big.