A nonstandard integer, or hyperinteger, is an element of the nonstandard extension 
of the integers. The ordinary integers embed in 
, but a proper nonstandard model also
contains infinite hyperintegers 
satisfying 
for every standard positive integer 
. Transfer gives 
the first-order arithmetic properties of 
. An infinite hyperinteger has no finite standard part.
Nonstandard Integer
See also
Hyperreal Number, Integer, Nonstandard AnalysisExplore with Wolfram|Alpha
References
Robinson, A. Non-Standard Analysis. Princeton, NJ: Princeton University Press, 1996.Cite this as:
Weisstein, Eric W. "Nonstandard Integer." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NonstandardInteger.html