This question has been asked before, but the title of the post was so general that it received no sufficient answer.
What is the cardinality of the set of jewels and reflected jewels in Indra's Net?
For those who don't know, Indra's Net is a poetic image used in Hindu and Buddhist cosmology to represent the universe. Imagine a grid-like net with a countably infinite amount of intersections and at each intersection there is a jewel. Now, on the surface of each jewel there are reflected images of every other jewel in the net. And since each of these reflected jewels is a copy of the actual jewels, they also have an infinite amount of reflected jewels within them. And within that second level of infinite reflected jewels, each of them also have infinite reflections... and so on, and so on, forever.
Basically, Indra's Net is like the scenario of two ideal mirrors facing each other, only the number of mirrors is countably infinite.
I've been trying to picture this with the number line. The integers could represent the original jewels, and the non-integer rational numbers could represent the first level of reflected jewels. Just pair each integer n with every rational number greater than n but smaller than n+1.
But then, each non-integer rational number would then have to be paired with its own distinct countably infinite group of numbers to represent the second level of reflection, and then every number representing that next level of reflection would in turn need its own distinct countably infinite group of numbers to be paired with, and so on, and so on.
Are there enough real numbers for this? The continuum always surprises me. Thank you.
EDIT: Reading the answers to the first version of this question made me realize how I underestimated the power of the old "1,2,3...".
Now, I have a similar question to my previous one, but I want to change the image of Indra's Net a bit. Imagine the standard image mentioned above, but then project the starting position infinitely "deep down" the levels of reflection so that not only do you see the standard Indra's Net before you, but as you look "outwards" you realize that your position is just one of infinitely many reflections within a larger meta-reflection, which itself is just a one reflection within an even larger meta-meta-reflection, and so on and so on, there being no "actual" jewels to begin with. You can "zoom-in" and "zoom-out" forever in both directions.
Is the cardinality of reflected jewels in this altered Indra's Net also the same as the set of integers?