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The question is probably very, very easily answered with basic mathematical facts about infinity. Does it have any bearing on philosophy, what the answer is?

  • A circle has no end and is not infinite. Did you mean "continuous"? If a process is "interrupted" it is, of course, no longer continuous, tautologically. – Conifold Aug 07 '22 at 08:08
  • yes, I definitely meant continuous, thanks @Conifold Does that make the question trivial? –  Aug 07 '22 at 08:09
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    Iteration on natural numbers is infinite and not continuous. – David Gudeman Aug 07 '22 at 09:43
  • yea that's simple thanks @DavidGudeman should I leave the question open? –  Aug 07 '22 at 09:44
  • curious to realise that an infinitely sized thing need not be everything that takes up space! right @DavidGudeman –  Aug 07 '22 at 10:02
  • The Fibonacci series is a discontinuous set of numbers and it is infinite. – RodolfoAP Aug 07 '22 at 10:28
  • @returning_binned_poster, I'm curious as to the asking of the question! Is there a particular conceptual problem you've come up against that this distinction would weigh in on? – Paul Ross Aug 07 '22 at 10:30
  • could be obviously a mistake or poorly phrased, if an infinite series of even discontinuous points is not infinitely sized. –  Aug 07 '22 at 10:33
  • honestly, I was just trying to fit in with the general feel of the site @PaulRoss so no puzzle just being cute –  Aug 07 '22 at 10:34

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You need to read up on infinity in philosophy (SEP link).

Infinity is a not infrequent topic on here, because it can help to get at issues around Mathematical Platonism, and the relationship between mathematics and science. Having said that, it's rarely a very productive topic, because really it comes down to definitions. But the status of mathematics is an important one in philosophy, with modern thinkers like Tegmark very much advocating for Platonism, while others like Deutsch & Marletto's Universal Constructor theory seems to imply a mathematical emergentism, a coarising of the universe and it's symmetries. I put my case for the status of mathematics here: The Unreasonable Ineffectiveness of Mathematics in most sciences

You choose the word 'process', implying an observation, something happening in the world. It can reasonably be argued no finite being can observe infinity, only infer it, because otherwise they would need infinite steps of observation, each involving a finite amount of time. Mathematics and science get around this through the process of taking the limit as a variable in a function approaches infinity, and that undergirds calculus. But that obscures the issue of mathematically undefined points, like 1/x at 0. We generally look to real conditions we are modelling, for how to deal with these points. It is certainly a position that many hold, to say infinities aren't in the world, only in maths, though. The same can be said of say circles, which are only idealised as continuous in an atomised world.

Conformal Cyclic Cosmology is a well considered proposition, that meets your criteria. The search for Hawking-points in the microwave background is on, so we don't know yet if the model is the case. But I'd say that means it is clearly possible for infinite processes to have discontinuities, because there is a spacetime discontinuity between universe iterations in the theory.

CriglCragl
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