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gams:operations_with_eps_and_inf

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# Operations with EPS and INF

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
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;
``` 