There are Hyperreal numbers that are smaller than any real number , also those that are larger than any real, they have properties analogous to those of Real numbers thanks to the Transfer principle and so on.
Then, It seems I could think of another kind of numbers that can be smaller or larger than any Hyperreal, and another kind that can be smaller or larger than any number of the former kind and one more ad infinitum. Is it correct or is it not? If not, how it'spossible to prove that ?
I recently took science of the existence of Hyperreal numbers after started studying calculus using Jerome Keisler's book, which is available here for free