Reading this wikipedia article on Lorentz transformations. It says that if $$ds^2=c^2 dt^2-dx^2-dy^2-dz^2$$ and $$ds'^2=c^2 dt'^2-dx'^2-dy'^2-dz'^2$$

then since one of them being zero implies the other must be zero implies that they are proportional because they are "of the same order." I've never heard this term in the context of infinitesimals - I searched the articles for differentials and for infinitesimals and couldn't find it. So what does it mean?

  • $\begingroup$ I believe it is just a statement about the fact that the two equations are homogeneous of degree 2. $\endgroup$ – Fabian Oct 10 '17 at 21:03
  • $\begingroup$ That's what I guessed it would be, was hoping someone would confirm $\endgroup$ – Eben Cowley Oct 10 '17 at 22:02

You may have been looking at the wrong wiki article. Try this. Cauchy was already familiar with infinitesimals of different orders (even though he never gave an epsilon-delta definition of continuity).


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