Hello I’m new here and firstly sorry for my English.
Following is a question from a discrete mathematics textbook.
Define a relation C from R to R as follows:
For any $(x,y) \in$ R $\times$ R
$(x,y) \in$ C means that $x^2+y^2=1$
Question: What are the domain and codomain of C
And the answer is:
The domain and co-domain of C are both R, the set of all real numbers.
Obviously we can draw the relation $x^2+y^2=1$ as a circle in the Cartesian plane whose radius is 1 and center is $(0,0)$.
I don’t understand why the domain is R rather than $[-1,1]$.
And I’ve learned that codomain is different from range that it can be large than range. But I still wonder could the the codomain of this relation be $[-1,1]$? Or any other interval which is larger than $[-1,1]$?
Really appreciated for you help!