I was thinking the other day about the difference between rational and irrational numbers, and wondering whether the distinction between them is created by leaving out discussion of precision.
So for instance people are calculating trillions of digits of pi (http://www.numberworld.org/misc_runs/pi-12t/).
However I found discussion of the limitation of pi based on planck's constant on quora:
Philosophically, it seems like PI the mathematical value is different from PI the engineering value.
Another area where I've seen this is in banking/lending. When you look at your bank account, it states the balance to two decimal points, whereas internally, from my experience banks keep account values to ten or more decimal points for the purposes of compounding interest.
Beyond the first hundred digits of PI, are the next trillion digits "real"? Similarly, are the digits of your bank account past the 2nd decimal place "real"? Saying "I have exactly two hands" seems to me to be "real". But saying "I walked exactly two miles" or "I poured exactly 1 teaspoon" seems like needs to include a precision metric with it.
So I think we need a philosophy of precision. Does this exist? I can't find any evidence of it on the internet