I'd be curious to hear a rigorous definition of physical reality for the rationals, IMO only the ones that are also integers have that property. Even those are

I'd be curious to hear a rigorous definition of physical reality for the rationals, IMO only the ones that are also integers have that property. Even those are debatable, owning discrete quantities of things is dependent on human sociocognitive constructs. The concept of the realness of the natural numbers is fundamentally linked to a human definition of realness rather than a first-principles approach like mathematical definitions. Discrete quantities do seem to exist in as fundamental a sense as anything can, but on small scales and also once you get beyond that you're stuck with probabilistic descriptions. 22/7 is exactly as real as pi, you just use different algorithms to evaluate them to the required degree of precision. When you try to examine the real world too closely using relative human terms like "exists," things get messy. It feels like I'm physically touching the keyboard keys as I type this but I'm not, it's field repulsion rather than physical contact (or rather, it turns out that what we call physical contact is not). It looks like I'm watching snowflakes swirl on the TV, but that's actually a series of still images exploiting meatspace processing limitations and not the continuous process of the real snowflakes falling outside my window - even though from here I can't really tell the difference. The delicious steaming mug of hot chocolate to my right doesn't actually taste like anything but warm river silt, the flavors are being processed by a different organ entirely. Our concept of reality is inexorably linked to how our brains process the signals around us, and every definition of "realness" I've seen based on human terms is weak.