The GAMS program below demonstrates some characteristics of EPS and INF. For more information see Non-standard analysis.
$Ontext All gams operations are defined over the closed interval from -infinity (-INF) to +infinity (INF) and the three other special values: epsilon (EPS), missing (NA) and undefined (UNDF). The model crazy in the GAMS Model Library demonstrates the definition of these special values. This example extends the demonstrates of EPS and INF. For more information see: http://en.wikipedia.org/wiki/Non-standard_analysis $Offtext Scalar s1,s2,s3,s4,s5,s6,s7,s8,s9; * infinitesimal * infinitesimal = infinitesimal s1=eps*eps; * infinitesimal * bounded = infinitesimal s2=eps*1E100; * infinitesimal / bounded = infinitesimal s3=eps/1E100; * infinitesimal + infinitesimal = infinitesimal s4=eps+eps; * infinitesimal - infinitesimal = infinitesimal s5=eps-eps; * infinity - infinity = 0 s6=inf-inf; * infinitesimal * 0 = 0 s7=eps*0; * infinitesimal / infinity = 0 s8=eps/inf; * bounded - infinitesimal = bounded s9=1-eps; display s1,s2,s3,s4,s5,s6,s7,s8,s9;