I asked a math PH.D. and they said Pi is an exact number. How can an irrational number be exact if we can't even reach the last digit ever? — TiredThinker
It is exact in the a priori intensional sense of being defined as an equation or algorithm with instantly recognizable form. — sime
a sequence of rational numbers — sime
pi as a constant is ambiguous — sime
Are any numbers exact? What is meant by 'exact'? — emancipate
An exact perfect circle can't be represented by an incomplete value of Pi? — TiredThinker
Pi is an exact number because it has one value: it is the length of a circle's circumference divided by its diamter. — Cuthbert
It is only exact in an ideal sense. — emancipate
In practical calculations, Pi is never exact. It's is just computed to a given precision. In C++, the value of Pi is 3.14159265358979323846, which is sufficient for most calculations. — pfirefry
I find 3.14 is sufficient for my practical purposes. — Metaphysician Undercover
intensional definition of pi — sime
The definition specifies a certain definite object. — TonesInDeepFreeze
Next time Elon needs some calculations to land a craft, he should just call you for your results rounded to two decimal points. — TonesInDeepFreeze
with 1/3 you poses all the information even if you can't write 3s forever — TiredThinker
Pi however can't be fully known. — TiredThinker
It must be more of a concept than a certain thing? — TiredThinker
Pi however can't be fully known. It is limited by our means to measure a circle physically or within a computer? It must be more of a concept than a certain thing? — TiredThinker
At least with 1/3 you poses all the information even if you can't write 3s forever. Or if you have a number system based on 6 instead of 10 it wouldn't need to go forever. — TiredThinker
Every mathematical object is an abstract concept and not a physical object. — TonesInDeepFreeze
What we cannot do is to measure pi exactly in the same way that we can count exactly. You can pick up exactly three apples and put back exactly two of them, leaving you with exactly one. But you can't measure out exactly pi kilos of sugar. If you happen to be holding exactly pi kilos of sugar then you can never know that is what you are holding. — Cuthbert
A true circle, as defined, is an impossible object to create — Metaphysician Undercover
The problem of the OP has turned out to be not specifically about pi. It is about the relationship between 'mathematical objects' and 'physical objects'. — Cuthbert
Every mathematical object is an abstract concept and not a physical object. — TonesInDeepFreeze
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