A point 
is said to lie between points 
and 
(where 
, 
, and 
are distinct collinear points) if 
. A number of Euclid's proofs depend on the idea of betweenness without explicit mentioning it.
All points on a line segment excluding the endpoints lie between the endpoints.
Let 
be a partially ordered set, and let 
. If 
, then 
is said to be between 
and 
. If 
in 
and there is no 
that is between 
and 
, then 
covers 
. Conversely, if 
covers 
, then no 
is between 
and 
