Hi, can anyone help me on these two problems? thank you so muchhhh..
1) Let D(n) denote the partially ordered set of positive integers d which divide n, and take the divisibility relation a l b to be the partial ordering. Prove that D(28) and D(45) are order-isomorphic, but the sets D(8) and
D(15) are not even though they have the same numbers of elements.
2) Let N be the nonnegative integers with the usual ordering, and take the lexicographic ordering on N X N. Prove that the linearly ordered sets N and
N X N have different order types. (hint: for each x in N, the set of all y such that y < x is finite).