I have problems with cardinals and their order.
Let K,L,M be sets so that card(K) = k, card(L) = l and card(M) = m.
Show that from the condition k < l does not follow, that
a) k + m < l + m
b) k*m < l*m
c) m^k < m^l
(Notice: the symbol is really "smaller than" not "smaller or as great as".)
I have tried to solve this for hours, and I really don't get a grip of it. Can anyone even help me to right direction?