(October 17, 2017 at 3:06 pm)RoadRunner79 Wrote:(October 17, 2017 at 2:34 pm)Jehanne Wrote: No, I am saying that the sum of those finite numbers (their ordinality) is infinite. But, once again, please answer my question, "Are some potential infinities bigger than others?"
I agree, that you can make up fractions potentially forever. However what they represent is still part of a finite thing. You are talking about the process.
I do think, that the more loosely define your set, then a infinite multi-dimensional array would be technically larger than and infinite single dimension array (such as used in addition).
How do you apply this to the topic?
Its seems, that you are talking about abstractions, not in any way reference to the two points of the OP. How do you connect these?
Do you see the logical contradiction with having an actual completed set, that is by definition never complete?
The set of natural numbers is an actual infinite, that is, it contains an infinite number of objects. Ditto for the set of real (rational and irrational) numbers, but in the latter case, that infinite set is larger than that of the natural numbers. How about "potential infinities?" Are they all the same size (cardinality)? Or, are some larger than others?
But, the point of my OP is that actual infinities may exist in nature, all around us, in fact. And, the simple act of motion is the traversal of an actual infinite, which means that the physical existence of actual infinities is not an absurdity.
