If c1 is an upper bound for A and c2 is an upperbound for B, then c1+c2 is an upperbound for A+B
Could anyone get me started? I can't seem to find the definition of A+B. Any help please?
Definitely its an upper bound, but it may not be the least upper bound. Lets take
A=sinx, c1=1(Least upper bound)
B=cosx, c2=1(Least upper bound)
A+B=sinx + cosx, for which least upper bound is √2 but not c1+c2=2.