1. ## help....please if someone could help me with this question....

i would really appreciate if someone could help me solve this problem for me....

Suppose that A and B are two non-empty bounded sets of real numbers such that x≤ y for every x є A and b є B
a) Show that the sets A = (6/7, 1) and B = { n/(n+1) l n є N } do not satisfy this condition.
b) Show that if A and B are two non-empty bounded sets that satisfy the condition, then supA ≤ infB
[N is set of natural numbers]

2. Originally Posted by qeetha8799
i would really appreciate if someone could help me solve this problem for me....

Suppose that A and B are two non-empty bounded sets of real numbers such that x≤ y for every x є A and b є B
a) Show that the sets A = (6/7, 1) and B = { n/(n+1) l n є N } do not satisfy this condition.

Well, $\displaystyle 61\slash 70 \in A\,,\,\,3\slash 4\in B\,,\,\,but\,\,\,61\slash 70>3\slash 4$ . On the other hand, $\displaystyle 61\slash 70<100\slash 101\in B$

b) Show that if A and B are two non-empty bounded sets that satisfy the condition, then supA ≤ infB
[N is set of natural numbers]

Apply the definition of supremum and the conditio.

Tonio