- #1
KataKoniK
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Q: Show that every bounded set in R has a least upper bound. Using either
"Every monotonic and bounded sequence is convergent" or
"Every bounded sequence has an accumulation point" or
"Every bounded sequence has a convergent subsequence"
I'm not really sure how to start this out, but would showing the statement true using a bounded compact set in R that has properties of those three statements be valid enough to show that R has a least upper bound (if this is alright, how would you show it mathematically?)? If not, then what would be the best way to show the statement is true? Thanks.
"Every monotonic and bounded sequence is convergent" or
"Every bounded sequence has an accumulation point" or
"Every bounded sequence has a convergent subsequence"
I'm not really sure how to start this out, but would showing the statement true using a bounded compact set in R that has properties of those three statements be valid enough to show that R has a least upper bound (if this is alright, how would you show it mathematically?)? If not, then what would be the best way to show the statement is true? Thanks.