If I were to come up with a function $f: \mathbb{N} \to \mathbb{N}$ that makes relation $R_a$ transitive yet non-reflexive and non-symmetric such that
$$q \, R_a \, z \text{ if } f(q) = z,$$ what kind of function should I come up with? I spent the past three hours trying to come up with one but I still don't understand how inputting one number can produce two different results… Do I need to use a piecewise?
Because isn't it transitive when you input $1$ and by some relation, you then get $2$.
Then when you input $2$ into that relation you get $3$.
Because of transitivity $1$ now should also produce $3$. This makes no sense to me…
Best Answer
How about $f(n)=17$ for all $n$?