The OP’s definition of a “true” number isn’t that it’s useful, meaningful or corresponding to something “real”. It’s merely that it’s objectively measurable and actually measured..
you come up with some numerical quantity, discover interesting facts about it, use it to analyze real-world situations—but never actually get around to measuring it. I call such things “theoretical quantities” or “fake numbers”,
It’s a specific failure mode that’s useful to talk about because it might let us recognize real-world failure in some “false” numbers. That’s not intended to imply there aren’t other failure modes; it’s not a sufficient test for the quality of a ‘number’.
The OP’s definition of a “true” number isn’t that it’s useful, meaningful or corresponding to something “real”. It’s merely that it’s objectively measurable and actually measured..
But why is this an interesting property that’s worthy of consideration?
It’s a specific failure mode that’s useful to talk about because it might let us recognize real-world failure in some “false” numbers. That’s not intended to imply there aren’t other failure modes; it’s not a sufficient test for the quality of a ‘number’.