Given a set A that contains all numbers of the form, n/(n+1), where n is a positive integer,
a.explain why the number 1.1 is not the lub of A.
b.explain why the number 0.95 is no the lub of A.
The Attempt at a Solution
a. Suppose 1.1 is the lub of A. Then it follows, from the least upper bound axiom, that
i. 1.1 is an upper bound of A and ii. 1.1≤y, if y is an upper bound for A. Since there exists y<1.1, such as y=1.01, we can see that l.l is not the lub of A. Thus, a contradiction.
(I'm not sure if I formatted this proof accurately (as I'm fairly new to proofs)).
b.It follows in a similar manner to a., although here I will show the first property of the lub isn't satisfied. That is, the number is not a upper bound.