Finding an upper bound that is not the supremum

  • #1
ver_mathstats
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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.
 

Answers and Replies

  • #2
PeroK
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Yes, any number greater than 1 would do.
 
  • #3
ver_mathstats
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Yes, any number greater than 1 would do.
Okay thank you.
 
  • #4
WWGD
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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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