I have this problem:
Show that there is exactly one greatest element of a poset, if such element exists.
I dont know if my proof is rigth:
Suppose that there are 2 greatest elements a and b in the poset(P,R).
thus, a R b and b R a -->a=b ( antisymetric). so it is unique.
Can someone someone correct me if I am wrong?
Now I will grant you that the may very well be a textbook that disagrees with all of the above. That is the curse of mathematical notation: nothing is standard.