Given Xn and Yn as bounded sequences in Reals, prove that:
a.) lim sup(Xn + Yn) <= lim sup(Xn) + lim sup(Yn)
b.) lim sup(Xn*Yn) <= lim sup(Xn) * lim sup(Yn)
Can someone explain how to go about proving these? Any help would be great. Thanks!
Given Xn and Yn as bounded sequences in Reals, prove that:
a.) lim sup(Xn + Yn) <= lim sup(Xn) + lim sup(Yn)
b.) lim sup(Xn*Yn) <= lim sup(Xn) * lim sup(Yn)
Can someone explain how to go about proving these? Any help would be great. Thanks!