I think what you mean here is that floating point numbers and the usual operators (+,*) and inverses (-,/) do not work the same as Reals (i.e. they don't form a

I think what you mean here is that floating point numbers and the usual operators (+,*) and inverses (-,/) do not work the same as Reals (i.e. they don't form a field), but people often behave as if they do. This is a common confusion.