“every full function is uniformly continuous”
That makes the distance inbetween important +numbers, Labels. Equidistance. The gap.
Physics uses Intuitionistic Logic and doesn’t usually realize it:
Smooth infinitesimal analysis
It’s the mathematics of infinitesimal calculus, brought forward to the 20th century by Anders Kock and Bill Lawvere under the name Synthetic Differential Geometry (SDG), or Smooth Infinitesimal Analysis. (I am too young to know exactly who invented what, but I’ve heard people say that Eduardo Dubuc also played a part. I would be happy to correct bibliographical omissions on my part.) By the way, I am not talking about Robinson’s non-standard analysis, which uses classical logic.
This is not the place to properly introduce synthetic differential geometry. I will limit myself to a few basic ideas and results. For a first reading I highly recommend John Bell’s booklet A Primer of Infinitesimal Analysis. If you refuse to read physical books, you may try his shorter An Invitation to Smooth Infinitesimal Analysis online. For further reading Anders Kock’s Synthetic differential geometry is an obvious choice (available online!), and there is also Moerdijk and Reyes’s Models of smooth infinitesimals analysis, which shows in detail how to construct models of SDG using sheaves of germs of smooth functions.”