Can someone help me with how to think about the below problem? I know that a poset is a relation which is reflexive, antisymmetric, and transitive, but unless I'm dealing with finite sets I have a lot of difficulty thinking through whether the properties fit.
Which of the following are posets?
- (a). $(R,=)$
- (b). $(R,|)$
- (c). $(Z^+,|)$
- (d). $(Z,\le)$
Looking at the Reals in (a), an arbitrary number 1.738 is always going to equal 1.738 in comparison, so it equals and relates to itself so is Reflexive. However, it isn't Antisymmetric?