You can introduce nonstandard analysis, but it's not necessarily incredibly intuitive either, even if you skip a formal construction (which requires either ultr

You can introduce nonstandard analysis, but it's not necessarily incredibly intuitive either, even if you skip a formal construction (which requires either ultrafilters or model theory). I think that's still a bit removed from just giving ad-hoc reasoning about "infinitely small" quantities without specifying precisely what you can and cannot do with them.