1. the notation in Definition 4.12 is hard to understand.
2. So Example 4.11 has demonstrated that i + sqrt(5) is enough to generate Q(i,-i,sqrt(5), -sqrt(5)). but with other situations, like if I have a (i)^(1/3), how do I tell if something is enough to generate all the needed elements?
the extension example shows that pi has a different type of irrationality than just square root of like 2 or 3?
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