Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

Am 08.10.2024 um 15:11 schrieb Alan Mackenzie:

I think infinity is understandable.  I think I understand it. 

"Conclusion
Properly understood, the idea of a completed infinity is no longer a problem in mathematics or philosophy. It is perfectly intelligible and coherent. Perhaps it cannot be imagined but it can be conceived; it is not reserved for infinite omniscience, but knowable by finite humanity; it may contradict intuition, but it does not contradict itself. To conceive it adequately we need not enumerate or visualize infinitely many objects, but merely understand self-nesting. We have an actual, positive idea of it, or at least with training we can have one; we are not limited to the idea of finitude and its negation. In fact, it is at least as plausible to think that we understand finitude as the negation of infinitude as the other way around. The world of the infinite is not barred to exploration by the equivalent of sea monsters and tempests; it is barred by the equivalent of motion sickness. The world of the infinite is already open for exploration, but to embark we must unlearn our finitistic intuitions which instill fear and confusion by making some consistent and demonstrable results about the infinite literally counter-intuitive. Exploration itself will create an alternative set of intuitions which make us more susceptible to the feeling which Kant called the sublime. Longer acquaintance will confirm Spinoza's conclusion that the secret of joy is to love something infinite."
(Peter Suber, Infinite Reflections)
Source: http://legacy.earlham.edu/~peters/writing/infinity.htm

My position is that the distinction between "potential infinity" and "actual
infinity" is bogus.  It makes no difference in mathematics, which is
probably why the terms have vanished from mathematical discourse.

Not quite. Finitism (if it's not ultrafinitism) is dealing with (or allowing for) "potential infinity" instead of "actual infinity".
"Finitism is a philosophy of mathematics that accepts the existence only of finite mathematical objects. It is best understood in comparison to the mainstream philosophy of mathematics where infinite mathematical objects (e.g., infinite sets) are accepted as existing."
Source: https://en.wikipedia.org/wiki/Finitism