I'm helping a friend with his homework, and the following problem is really giving us both trouble.
Consider the subset of given by . Give the partial order defined by if and only if and , where is the usual order on .
I'm good so far, but this is the part that has me stumped:
Find a set in which has no infimum.
It seems to me that any finite subset of would have an infimum.
(It should be noted that the book that this problem came from is well known for its typos and wrong answers in the student solutions section.)