question archive Let A and B be a bounded set
Subject:MathPrice: Bought3
Let A and B be a bounded set.
sup(A union B)=max{sup A, sup B)
I am struggling with the proof
Let x belongs to A to B, then x belongs to A or x belongs to B
x<= sup A, x<= sup B
It means x<=max(sup A, sup B)
i am struggling with the next step
when x<=max(sup A, sup B) implies sup(AUB)<=max (sup A, sup B)
I know that x<=sup(AUB), but I don't know why sup (A U B )<= max (Sup A, sup B)