Abstract or not, the number concept originates from the world, so it seems to me there are only as many numbers as things, and there comes a point where what we call numbers are only hollow representations, pointing at concepts which are false in the edge cases, and so false in themselves.
If there were 2 things in the universe, then 3 wouldn't be a number, even abstractly, because the abstract is a representation of reality, isn't it? Even if not, it still caries truth/false in the abstract.
I read this nice topic about it, which is closed
Yes, to mathematicians, infinity is countable, because you can theoretically start at 0, count upwards 1, 2, 3, 4, 5... and "reach" ℵ₀ according to the axiom of induction.
But counting is a concept which originates from grouping things. So even in theory, there comes a point where we can't count, if we can't count in reality by adding an item to such number of things.
There is counting-counting, then there is playing with notation.
I don't think the induction follows. Do we think theory has validity just because the notation plays nice?
It seems to me, Zeno's paradox could even be seen as a proof of the finiteness of numbers, because even in the abstract we reach the paradox of the true abstract (there are arrows which can be shot) against the false abstract (it can be divided in an infinite set of motions). Something has to give in.
I know we gave in in thinking that we can sum infinities... Well, I don't give in there. We can't sum infinite sums, because there are no infinite sums to sum.
A representation is true in the extent of the truthness of what it represents. If I add 1 unicorn to 1 unicorn, I get 2 unicorns, because the false representing unicorns are represented by real 1 thing and 1 thing counting... So the abstract numbers are only true representations in the extent of the truthness of the real things they represent. Then they become unicorns which fail in the edge cases, like being.
If it is not being, then it is a false concept, and the infinity of number is a false concept, so it is false.
Even in the abstract, numbers are finite. I can't imagine a new color, can I? The limit of representation. There is no real unicorn concept, only the concepts of horse, corn, and the shapes/sounds. It is concepted artificially, partially, so it is not even a concept, but a meshing of concepts (themselves wholly concepted from reality, so wholly true), through the mesh concept, into a false, void 'concept'. In the same way, there is no concept, for some numbers, and for infinity. It's only playing with notation.
Infinity exists only as much as we can put "in" in front of "finity", and wonder why it doesn't mean anything we can visualize. We can't represent it, because it doesn't exist, even abstractly. It is false.
Well, that's just, like, my opinion