Antisymmetry and Totality implies Reflexivity One can check that antisymmetry and totality imply re
exivity. Thus,
a totally ordered set is equivalent to a partially ordered set in which the binary
relation is total.
I am reading Khovanov's notes for Representation theory of finite groups, and confused by this statement. Can someone help me understand this. Thank you very much!

Let $X$ be a set and $R \subseteq X \times X$ be a binary relation on $X$. We say that:


*

*$R$ is reflexive if $x \, R \, x$ for all $x \in X$;

*$R$ is antisymmetric if, for all $x, y \in X$, if $x \, R \, y$ and $y \, R \, x$ then $x = y$;

*$R$ is total if, for all $x, y, \in X$, either $x \, R \, y$ or $y \, R \, x$.


If $R$ is total then $R$ is reflexive (notice that antisymmetry is not needed). Indeed, given $x \in X$, by totality (take $y = x$) either $x \, R \, x$ or $x \, R \, x$, i.e. $x \, R \, x$.
