Finding an upper bound that is not the supremum

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Homework Help Overview

The discussion revolves around the concept of upper bounds in the context of the interval (0,1) and its supremum, which is 1. Participants are exploring the relationship between upper bounds and the supremum, specifically identifying an upper bound that is not the supremum.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the validity of identifying 2 as an upper bound for the interval (0,1), while noting that the supremum is 1. There is an exploration of the definition of supremum as the least upper bound.

Discussion Status

There is a general agreement among participants that any number greater than 1 can serve as an upper bound. Some participants provide clarification on the definition of supremum, indicating a productive exploration of the concept.

Contextual Notes

Participants are operating under the assumption that the definition of supremum is understood, and they are questioning the implications of identifying upper bounds beyond the supremum.

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Homework Statement
Let S=(0,1), find a real number M which is an upper bound of S, but M is not the supremum of S.
Relevant Equations
S=(0,1)
I just want to see if I did this correctly, the interval (0,1) has 2 as an upper bound but the supremum of S is 1. So M would be equal to 2?

Thank you.
 
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Yes, any number greater than 1 would do.
 
PeroK said:
Yes, any number greater than 1 would do.
Okay thank you.
 
Just to expand a bit. The Supremum is , by definition/construction, the _Least_ Upper Bound. This implies any other upper bound should be greater than the Sup, as @PeroK wrote.
 

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