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I would claim that infinity and repetition have nothing to do with one another at a basic level, but that every human representation of infinity can only be made via repetition.

We have only finitely many symbols to work with, and via them we can define only countably many things with clarity. We can define the integers, and give each of them a unique representation, and go from there to the rationals, and from there to all algebraic roots of rational polynomials, and from there to all closed integral forms with bounds among those algebraically identified numbers, etc. etc. etc. After a countably infinite number of layers, we could eventually have a representation for every real number, in theory.

But if we really want to write down an allusion to infinity, it has to be in terms of a finite set from among this tower of more-and-more complex representations, and beyond that, if it is really going to be deterministic, it has to be captured in some finite algorithm that would write out the rest of the representations to which we are alluding. Therefore loops or recursion, and therefore repetition.

When we think that the points of the real line all 'look the same', it is because the vast majority of them cannot have names that would focus our attention on them in a way that would make a difference. But this is an illusion forced on us by language. We cannot capture the detail in any meaningful way with finitely many symbols.

(From a constructivist point of view, that means most of those points do not exist, and everything is finite with a single countable iteration represented as a process. Infinite constructs are useful for projecting concepts onto, but if you cannot construct the results, you have no object. From that point of view, all infinities are countable, and inaccessible. So in that frame of mind (which I manage at my best), your observation is correct.

Still, being correct in reality and being correct in principle are not the same, this association is false in principle.)

I would claim that infinity and repetition have nothing to do with one another at a basic level, but that every human representation of infinity can only be made via repetition.

We have only finitely many symbols to work with, and via them we can define only countably many things with clarity. We can define the integers, and give each of them a unique representation, and go from there to the rationals, and from there to all algebraic roots of rational polynomials, and from there to all closed integral forms with bounds among those, etc. etc. etc. After a countably infinite number of layers, we could eventually have a representation for every real number, in theory.

But if we really want to write down an allusion to infinity, it has to be in terms of a finite set from among this tower of more-and-more complex representations, and beyond that, if it is really going to be deterministic, it has to be captured in some finite algorithm that would write out the rest of the representations to which we are alluding. Therefore loops or recursion, and therefore repetition.

When we think that the points of the real line all 'look the same', it is because the vast majority of them cannot have names that would focus our attention on them in a way that would make a difference. But this is an illusion forced on us by language. We cannot capture the detail in any meaningful way with finitely many symbols.

I would claim that infinity and repetition have nothing to do with one another at a basic level, but that every human representation of infinity can only be made via repetition.

We have only finitely many symbols to work with, and via them we can define only countably many things with clarity. We can define the integers, and give each of them a unique representation, and go from there to the rationals, and from there to all algebraic roots of rational polynomials, and from there to all closed integral forms with bounds among those algebraically identified numbers, etc. etc. etc. After a countably infinite number of layers, we could eventually have a representation for every real number, in theory.

But if we really want to write down an allusion to infinity, it has to be in terms of a finite set from among this tower of more-and-more complex representations, and beyond that, if it is really going to be deterministic, it has to be captured in some finite algorithm that would write out the rest of the representations to which we are alluding. Therefore loops or recursion, and therefore repetition.

When we think that the points of the real line all 'look the same', it is because the vast majority of them cannot have names that would focus our attention on them in a way that would make a difference. But this is an illusion forced on us by language. We cannot capture the detail in any meaningful way with finitely many symbols.

(From a constructivist point of view, that means most of those points do not exist, and everything is finite with a single countable iteration represented as a process. Infinite constructs are useful for projecting concepts onto, but if you cannot construct the results, you have no object. From that point of view, all infinities are countable, and inaccessible. So in that frame of mind (which I manage at my best), your observation is correct.

Still, being correct in reality and being correct in principle are not the same, this association is false in principle.)

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I would claim that infinity and repetition have nothing to do with one another at a basic level, but that every human representation of infinity can only be made via repetition.

We have only finitely many symbols to work with, and via them we can define only countably many things with clarity. We can define the integers, and give each of them a unique representation, and go from there to the rationals, and from there to all algebraic roots of rational polynomials, and from there to all closed integral forms with bounds among those, etc. etc. etc. After a countably infinite number of layers, we could eventually have a representation for every real number, in theory.

But if we really want to write down an allusion to infinity, it has to be in terms of a finite set from among this tower of more-and-more complex representations, and beyond that, if it is really going to be deterministic, it has to be captured in some finite algorithm that would write out the rest of the representations to which we are alluding. Therefore loops or recursion, and therefore repetition.

When we think that the points of the real line all 'look the same', it is because the vast majority of them cannot have names that would focus our attention on them in a way that would make a difference. But this is an illusion forced on us by language. We cannot capture the detail in any meaningful way with finitely many symbols.