It has been a while since i am occupied in some thoughts and a couple of literary works, with the double nature of the infinity understandable by humans.
The two infinites are the following:
1)The infinite seen as an endless collection of smaller parts, giving when added up a finite sum
An example of this is the progression of numbers like 1+1/2+1/4+1/8+...1/n=2. It almost equals 2, but we have added infinite numbers to reach this finite result.
This type of infinity understanding is the basis for Zeno's paradoxes, where one never gets to the end of a finite space or time, since in order to do that he would have to go through infinite parts.
2) The infinite seen as a collection of parts, giving an infinite sum
An example of this is the addition of all the natural numbers (1+2+3+4+....n). It is at the same time an infinite sum, and one giving an infinity as a result.
This type of infinity understanding is what enables us to draw infinite shapes, and realize them as finite. For example any kid can draw a line on a blackboard, because it views it as finite. In reality it is a sum of infinite parts. The circle can also be drawn, while it is at the same time infinite and periodically repeated.
Since i am thinking of concluding a larger literary work with this subject, i felt like asking you if you have any thoughts about this double nature of our understanding of infinity. While infinity is studied in math, i think the question as to how we can have these two antithetical examinations of it is not answered at all.
Looking forward to your views.