My question is pretty simple, but I want to make sure I'm understanding it correctly, because otherwise my misconception could go on a while.
What is the "order type" of [0,1)?
I know the set has a smallest element, does not have a largest element, and for any two elements in the set x < y we can find another element z so that x < z < y.
Are these the properties referred to by the phrase "order type of [0,1)"? Is there anything I am missing?
This was inspired by a homework problem from Munkres #12 from section 24 needing to show that [a,c) has the same order type as [0,1) iff both [a,b) and [b,c) have the same order type as [0,1).