[taeric]

I think the consequences of what you are saying makes sense. Would be neat to explore more of the idea. I was starting to find, recently, that it was better to think of numbers as symbols that follow operational rules. This view seems counter to that.

[analog31]

There is a view that math is "just" symbol manipulation. So I can't say your approach is wrong. Probably whatever works, works.

And you can usefully say things like "x is a number" without saying which particular number x is.