The infimum is the greatest lower bound of a set, defined as a quantity such that no member of the set is
less than ,
but if is any positive
quantity, however small, there is always one member that is less than (Jeffreys and Jeffreys 1988). When it exists (which
is not required by this definition, e.g., does not exist), the infimum is denoted or .
The infimum is implemented in the Wolfram
Language as MinValue[f,
constr, vars].
Consider the real numbers with their usual order. Then for any set , the infimum exists (in ) if and only if is bounded from below
and nonempty.
More formally, the infimum
for a (nonempty) subset
of the affinely extended real numbers is the largest
value such that for all we have . Using this definition, always exists and, in particular, .
, defined as a quantity 
such that no member of the set is
less than 
,
but if 
is any positive
quantity, however small, there is always one member that is less than 
(Jeffreys and Jeffreys 1988). When it exists (which
is not required by this definition, e.g., 
does not exist), the infimum is denoted 
or 
.
The infimum is implemented in the Wolfram
Language as MinValue[f,
constr, vars].
, the infimum 
exists (in 
) if and only if 
is bounded from below
and nonempty.
for 
a (nonempty) subset
of the affinely extended real numbers 
is the largest
value 
such that for all 
we have 
. Using this definition, 
always exists and, in particular, 
.
