Infinitesimal angular displacement ?

[abcdefg10645]

How can we proved that the infinitesimal angular displacement is a vector mathematically ?

Or~how can we prove that a non-infinitesimal angular displacement is not a vector ?

 

[ideasrule]

This sounds suspiciously like a homework question. If it is, it should really go in the "Homework and Coursework" section.

I'll get you started on this problem: what are the properties of vectors? Do non-infinitesimal angular displacements obey these properties? How about infinitesimal displacements?

 

[abcdefg10645]

It's NOT a homework first ~

And I am not satisfied with the proof I saw before ~

The proof I saw is based on the commutative of a vector ~

I'm now seeking for a new proof which make sense!