Actually, I don't really see what is wrong with having several
"versions" of sqrt(6). Clearly the one inside C and the one inside R
should know about each other / be the same. But what about the element x
of the quotient ring QQ[x]/(x^2 - 6)? Surely they should not, a priory,
be the same?
Your x is an equivalence class of polynomials, it's not sqrt(6). You
can't say that x> 2 or that log(x) == log(6)/2.
All points I would also have made. I just wanted to be sure :).
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