Thread: Real Numbers

Mark each true or false and justify.

1) If a nonempty subset of real numbers has an upper bound, then it has a least upper bound.

2) Every nonempty bounded subset of real numbers has a maximum and a minimum.

3) If m is an upper bound for S and m' < m, then m' is not an upper bound for S.

4) For each real number x and each E > 0, there exists an n element of the natural numbers such that nE > x.

Originally Posted by noles2188

1) If a nonempty subset of real numbers has an upper bound, then it has a least upper bound.

How about ?

2) Every nonempty bounded subset of real numbers has a maximum and a minimum.

How about ?

3) If m is an upper bound for S and m' < m, then m' is not an upper bound for S.

How about and and ?

4) For each real number x and each E > 0, there exists an n element of the natural numbers such that nE > x.

Yes