Full Idea
Non-standard natural numbers will yield non-standard rational and real numbers. These will include reciprocals which will be closer to 0 than any standard real number. These are like 'infinitesimals', so that notion is not actually a contradiction.
Gist of Idea
Infinitesimals are not actually contradictory, because they can be non-standard real numbers
Source
David Bostock (Philosophy of Mathematics [2009], 5.5)
Book Reference
Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.155