Rational numbers - bounded subset with no least upper bound

ciarax
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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?
 
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ciarax said:

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.
 
ciarax said:
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.
 

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