Z attach x, what is the name of this?

[TylerH]

I'm trying to reveiw the concepts of a proof class I took last summer, and there's one thing that's killing me. What is it called and what's the notation used when you "attach" something to a set. For example, my professor would define "the integers attach √2" as the set {a+b√2 : a, b in Z} or the complex numbers as "the real numbers attach i."

Thanks,
Tyler

 

[Stephen Tashi]

That looks like a "field extension". http://en.wikipedia.org/wiki/Field_extension

 

[TylerH]

YES! Thank you.

Is the "attach" verbal notation common? It isn't mentioned on the Wikipedia page. How do you usually say Z(i)?