Let $\emptyset \neq A \subset \mathbb R$ be bounded above in $\mathbb R$. Let $B$ be the set of upper bounds of $A$. Show that B is bounded below and $\operatorname{lub} A = \operatorname{glb} B$
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Welcome to Stack Exchange! It would be helpful for you to post your ideas on the problem so far, so we can give more useful responses. – B. Mehta Oct 31 '17 at 11:08
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Please see How can I format mathematics here? in our Help Center and pages linked there. – CiaPan Oct 31 '17 at 11:09
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Namaskar Mehta ji – Abhishek Pal Oct 31 '17 at 11:13
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Consider following two cases: $A= (-\infty, 0)$ and $A=(-\infty, 0]$. What is $B$ in these two cases? Try to solve these two cases explicitly. That will give you an idea how to solve the stated problem. – Krish Oct 31 '17 at 11:38
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we can not take any cases because we have solve generaly . – Abhishek Pal Oct 31 '17 at 11:38
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@AbhishekPal These are test cases (examples, if you prefer) to get an idea on the approach of the general problem. – Krish Oct 31 '17 at 11:43
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plz give proof of it – Abhishek Pal Oct 31 '17 at 11:45