Hi there. Firstly, sorry if the title wasn't overly descriptive.
I'm working on an assignment question dealing with group/ring theory that is:
Let be the ring of all real-valued functions defined on the closed interval [0, 1]. Decide if the folowing subset of R is a subring of R:
has an infinite number of solutions in [0, 1]
I know since it is already a subset of R that I need to check if:
So basically whether
will also have an infinite number of solutions.
Another question was similar but the subset consisted of the functions of R that had only a finite number of solutions in [0,1]. I was able to determine by contradiction using an example that it indeed was not, so my intuition here is that this subset is a subring. I'm just not sure how to start it.
Thanks for any help,
In order to be a ring doesn't it just have to be associative under addition and multiplication, commutative under addition, 0 and negatives exist, and obey the distributive law? A ring with unity (identity element) is in addition to a basic ring I thought.
I could be completely wrong however and any clarification would help my understanding!
Thank you as well for your help Tonio. Really appreciate it.