![[Maple Math]](images/lnotes1681.gif){kind=small}
is said to be convex if whenever (
![[Maple Math]](images/lnotes1682.gif){kind=small}
) and (
![[Maple Math]](images/lnotes1683.gif){kind=small}
) belong to
![[Maple Math]](images/lnotes1684.gif){kind=small}
, all points on the line segment
![[Maple Math]](images/lnotes1685.gif){kind=small}
with
![[Maple Math]](images/lnotes1686.gif){kind=small}
in the interval
![[Maple Math]](images/lnotes1687.gif){kind=small}
, belong to the set
![[Maple Math]](images/lnotes1688.gif){kind=small}
as well.
Definition (convex set)
A set
is said to be convex if whenever (
) and (
) belong to
, all points on the line segment
with
in the interval
, belong to the set
as well.
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