anonymous
  • anonymous
Let A and B be nonempty bounded subsets of the real numbers. a ) Explain why the union, AUB has a supremum.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
for supremum to exist, the sets should be bounded from above and are nonempty. Since the question said that we have 2 bounded non-empty sets and since A and B are both subsets of R (all real numbers), then we say that A U B has a supremum hmm, I hope this made it clear for you :)
anonymous
  • anonymous
Moreover, no matter how many elements are found in AUB , they're still less than the Real number sequence, so that's why AUB has a supremum ^_^

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