[farrelle25]

That's interesting - I read something similar in Bell's 'A primer of infinitesimal analysis' where he said the price for 'Smooth World' infinitestimals is giving up the Law of Excluded Middle (LEM).

Don't really understand why (he said something about unconstrained use of LEM allows discontinuous functions...)

Is there any link to Brouwer's Intuitionism where LEM is rejected too (?!)

Ah it's all an interesting can of worms...

[Ericson2314]

https://ncatlab.org/nlab/show/real+numbers+object you can definitely have real numbers without the infinitesimals in constructive math, however.