MHB Are Non-Ordered Numbers More Than Complex Numbers?

[highmath]

1. The complex number are not ordered. Which else number are not ordered?
2. Are the infinitesimally numbers are ordered numbers? It there a difference between infinitesimally number to another infinitesimally number?

 

[topsquark]

1. The complex number are not ordered. Which else number are not ordered?
2. Are the infinitesimally numbers are ordered numbers? It there a difference between infinitesimally number to another infinitesimally number?

I'm not going to write it out again. Please see your question here. If you don't understand the response please say so on this or the other site.

-Dan

 

[I like Serena]

1. The complex number are not ordered. Which else number are not ordered?

Other examples: Quaternion numbers ($\mathbb H$), Octonion numbers, Gaussian integers ($\mathbb Z(i)$), integers modulo $n$ ($\mathbb Z_n=\mathbb Z/n\mathbb Z$ or $F_n$).

2. Are the infinitesimally numbers are ordered numbers? It there a difference between infinitesimally number to another infinitesimally number?

Yes.
Let $\varepsilon$ be a positive infinitesimal, and let $\omega=\frac 1\varepsilon$ be the corresponding infinity.
Then:
$$2<2+\varepsilon<2+2\varepsilon<\frac\omega 2<\omega-\varepsilon<\omega<\omega+1+\varepsilon$$

 

[HOI]

By the way "infinitesimally", ending in "ly", is an adverb and cannot modify a noun like "numbers". The corresponding adjective is "infintesmal" You want to talk about "infinitesimal numbers" not "infinitesimally numbers".