Pi can be exact if we have a new number system.
Wanna expand on that?
We already have an exact representation of pi: "pi".
So what is your exact idea about this ?
What do you think if we do create a new number system to make Pi and e rational, but 1/2 is irrantional number?
Obviously, we could choose pi itself as a base for our numeration system so that pi would be "1.0". Since pi and e are algebraically independent, I don't believe it is possible to choose a base so that pi and e are both represented by finite or repeating decimals. It is fairly easy to show that a number is "rational" in an INTEGER based numeration system if and only if it is "rational" in any INTEGER based numeration system but I'm pretty sure that all the rational numbers in an INTEGER based numeration system (e.g. base 10) would be "irrational" in a pi based numeration system.
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