I'm having some trouble understanding one of the specific parts of the following definition, I was just wondering if someone can clarify me on this point.
The definition I have is a set $X$ is well-ordered by the relation $R$ if the following principles hold:
$(1)$ For every $x$ and $y$ in $X$, if we have $xRy$ then we cannot have $yRx$. this means that $R$ is asymmetric on $X$.
$(2)$ For every $x$ and $y$ in $X$, exactly one of $xRy$,$yRx$ and $x=y$ holds. This means that $R$ is connected on $X$.
$(3)$ For all $x$,$y$ and $z$ in $X$, if $xRy$ and $yRz$, then $xRz$. this means that $R$ is transitive on $X$.
$(4)$ Every non-empty subset of $X$ has an $R$-least element.
My confusion is with the 4th property I don't understand what it means by $R$-least element if someone could clarify this that would be great.
Let $Y \subseteq X$. We say $y \in Y$ is $R$-least in $Y$ in case $yRy'$ for all $y' \neq y$, and $y \in Y$.
This terminology is inspired by the case where $aRb$ means "$a$ is less than $b$."