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A comment on List of Statements Independent of ZFC. Parent comment

Re:List of Statements Independent of ZFC by Filligree on Wednesday December 18, 2019 @07:22PM (#21830907)
All of calculus.
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Re:List of Statements Independent of ZFC by roywiggins on Wednesday December 18, 2019 @08:02PM (#21831146)
It's possible to do quite a lot without infinities in calculus and trigonometry, whether it makes sense to bother is another question.

https://en.m.wikipedia.org/wiki/Rational_trigonometry

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Re:List of Statements Independent of ZFC by Cogito on Wednesday December 18, 2019 @11:28PM (#21832006)
> It's possible to do quite a lot without infinities in calculus and trigonometry

This is like Stacey King saying "I'll always remember this as the night that Michael Jordan and I combined for 70 points."

Pretty much the entire field of Analysis (of which calculus is a part) relies on 'infinities' of some kind. Even if you try to restrict to the rationals, you're still typically working with infinite series of them.

You can do some analysis over the rationals, but often this takes the form of Cauchy sequences of rationals which might be cheating.

[0] https://math.stackexchange.com/questions/387234/how-far-can-...

[1] https://www.dpmms.cam.ac.uk/~wtg10/reals.html

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