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A set has the ''least upper bound property'' if every set that has an upper bound has a least upper bound.  There is also a ''greatest lower bound property'', and any reasonable set having one property has the other.

A set has the ''least upper bound property'' if every set that has an upper bound has a least upper bound.  There is also a ''greatest lower bound property'', and any reasonable set having one property has the other.

The least upper bound property is extremely important in caclulus and analysis.  It is essential for many theorems, notably the ''[[mean value theorem]]'' and the ''intermediate value theorem''.

The least upper bound property is extremely important in calculus and analysis.  It is essential for many theorems, notably the ''[[mean value theorem]]'' and the ''intermediate value theorem''.

::''The rational numbers do not satisfy the least upper bound property.''

::''The rational numbers do not satisfy the least upper bound property.''