Hyperreal numbers on the ultrafilter extending the cofinite filter

A sample infinitesimal hyperreal

A sample infinite hyperreal

Standard part predicate

Standard part function: like a "round" to ℝ instead of ℤ

A hyperreal number is infinitesimal if its standard part is 0

A hyperreal number is positive infinite if it is larger than all real numbers

A hyperreal number is negative infinite if it is smaller than all real numbers

A hyperreal number is infinite if it is infinite positive or infinite negative