According to definition of Hyperreal numbers
The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form 1 + 1 + 1 + ...... + 1.[this definition has been extracted from wiki encyclopedia Hyperreal number]
According to above statement Hyperreal numbers include only infinite numbers and doesn't include their reciprocals, infinitesimals(correct me if I am wrong in saying this).
I have come across another statement mentioned in the same wiki encyclopedia which states that
The idea of the hyperreal system is to extend the real numbers R to form a system *R that includes infinitesimal and infinite numbers, but without changing any of the elementary axioms of algebra.[this statement has been extracted from wiki encyclopedia Hyperreal number/The transfer principle]
According to above statement Hyperreal numbers include both infinitesimal and infinite numbers,which contradicts the definition of Hyperreal numbers.So,what does it mean?Do Hyperreal numbers include infinitesimals?