Rational numbers - bounded subset with no least upper bound

[ciarax]

Homework Statement

Give an example of a bounded subset of Q which has no least upper
bound in Q. Explain why your answer has this property.

Homework Equations

The Attempt at a Solution

[1/8, 1/4, 3/8, 1/2, 5/8, 3/4...infinity]
is this correct?

 

[LCKurtz]

Homework Statement

Give an example of a bounded subset of Q which has no least upper
bound in Q. Explain why your answer has this property.

Homework Equations

The Attempt at a Solution

[1/8, 1/4, 3/8, 1/2, 5/8, 3/4...infinity]
is this correct?

No. Hint: What kind of numbers are missing from Q? Find a bounded set that has one of them for its lub.

 

[Mark44]

Give an example of a bounded subset of Q which has no least upper
bound in Q. Explain why your answer has this property.

[1/8, 1/4, 3/8, 1/2, 5/8, 3/4...infinity]

Your set appears to be integer multiples of 1/8. This set is not bounded, so doesn't qualify as an example in this problem.