Dieudonne on Dedekind

Arnold Neumaier arnold.neumaier at univie.ac.at
Wed Aug 11 02:27:43 EDT 2021

On 11.08.21 04:24, Timothy Y. Chow wrote:
> It's true that this is close to how professional mathematicians tend
> to view the matter.  Dedekind cuts or Cauchy sequences are used to
> prove existence, but once you've done that, you forget about the
> existence proof and just use the axioms.
> I'm not sure how I feel about this attitude.  It's certainly a
> pragmatic one---you can cover more material this way, and the students
> who don't see the point of the existence proof are spared the torture
> of being dragged through it.  On the other hand, as a fan of f.o.m., I
> can't help but feel some pangs of conscience about knowingly leaving a
> gaping hole in the foundations of the subject, right around the time
> that most students are just beginning to understand what rigorous
> proof is.

A gaping hole in undergrad education is unavoidable. Dedekind's proof
only moves the gaping hole from the foundations of real numbers to the
foundations of set theory.

More information about the FOM mailing list