Q:

Give an example of a relation $R$ that is a total injective function from a set $A$ to itself but is not bijection?

Give an example of a relation $R$ that is a total injective function from a set $A$ to itself but is not bijection.
This is problem from  Mathematics for Computer Science(chrome-extension://ikhdkkncnoglghljlkmcimlnlhkeamad/pdf-viewer/web/viewer.html?file=https%3A%2F%2Fcourses.csail.mit.edu%2F6.042%2Fspring17%2Fmcs.pdf) in page 126

A:

$R = \{ (n,2n) | n \in \mathbb{N} \}$ will do.  I'll leave it to you to prove it is total, injective, but not bijective.

