To start off on the right foot. I've read: Relations (Binary) - Composition but I still can't really figure it out because those deal with finite sets. I have a infinite set:
$R= \{(n,n+2)|n \in \mathbb{N}\}$
Which is composed with itself. I tried applying the concept of there being one element in common in $R∘R$ such that $(x, z) \in R$ and $(z, y) \in R$. Are there multiple answers?
I figured that the composition of $R$ doesn't exist,
Because if: $x = n$ and $y = n+2$. Then $z$ must be both $n+2$ and $n$. Which is not possible.
If someone could point me in the right direction that would be awesome.
Thanks in advance!
Yes, regarding your revelation, sort of. That is, in this case, we have $$R\circ R = \{(n, n+4) \mid n\in \mathbb N\}$$
$$x\in \mathbb N \overset{R}{\longrightarrow} x+2 \overset{R}{\longrightarrow} (x+2)+2 = x+4\in \mathbb N$$