No I'm not. There are lot of ways to construct the integers. One is to use the unit value and a generating function and form the closure under that function. Another even more common way is to use the successor function S, and start with (usually) 0.

You seem inordinately focused on the superficial aspect of different ways you might choose to represent numbers with a limited symbol set. But that's completely superficial. It doesn't matter whether you write 9 or IX or 1001 or 1+1+1+1+1+1+1+1+1 or SSSSSSSS0.

It seems like you're wanting to make abstractions, which is good, but you're trying to come up with your own, and they're very simple. I think you would be better served by understanding the kinds of abstractions in more depth, not in the apparently very shallow analogical level you do.

For instance, I don't think there's any real content behind the phrase "Gravity is the synergistic outcome of the other forces." Does this explain the relative strength of the forces? Does it explain why gravitation falls off as 1/r^2 but the strong interaction falls off incredibly fast?