Perhaps a translation issue?
I've always referred to that set as "algebraic numbers" ( https://en.wikipedia.org/wiki/Algebraic_number ). Since they are equipotent with integers, you _can_ call them that, but it's misleading.
I've always referred to that set as "algebraic numbers" ( https://en.wikipedia.org/wiki/Algebraic_number ). Since they are equipotent with integers, you _can_ call them that, but it's misleading.
Algebraic integers are much cooler, since there is a number theory on them: https://en.wikipedia.org/wiki/Algebraic_integer . (And also because the most basic facts about it, like that it forms a ring, are not trivial to prove, that's a good sign for a concept to be cool and useful.)
These two number sets are more or less in a relationship like regular integers (with a number theory), and rational numbers. In fact A = O/Z where A denotes the set of algebraic numbers, O denotes the set of algebraic integers, and Z denotes the set of integers.
I like teaching this kind of stuff to my grade 9 and 10 advanced math classes. It’s not that hard to understand and yet it gives students a sense of wonder about how math works. I might try to show the grade 10s algebraic integers now.