query: How can I prove that $\inf B=\sup A$?
positive_passages.docid: 152817
positive_passages.text: Proving $\sup B=\inf A$
negative_passages.docid: 98855
negative_passages.text: Prove $aba^{-1}b^{-1}\in{N}$ for all $a,b$
negative_passages.docid: 50142
negative_passages.text: If sup A $\lt$ sup B show that an element of $B$ is an upper bound of $A$
negative_passages.docid: 69184
negative_passages.text: Proof that absolute value of supremum equals suprememum of absolute value
negative_passages.docid: 129480
negative_passages.text: Prove that inf(A+B) = infA + infB
negative_passages.docid: 138199
negative_passages.text: Proof explanation $A\setminus B = A \setminus B \cap A$
negative_passages.docid: 87239
negative_passages.text: Prove functions defined by sup and inf are continuous
negative_passages.docid: 87536
negative_passages.text: Supremum of the infimum
negative_passages.docid: 26741
negative_passages.text: How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
negative_passages.docid: 150738
negative_passages.text: Proof of $(A - B) - C = A - (B \cup C)$
negative_passages.docid: 53857
negative_passages.text: Showing $\sup \{ \sin n \mid n\in \mathbb N \} =1$
negative_passages.docid: 27281
negative_passages.text: How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
negative_passages.docid: 42809
negative_passages.text: How can we show that $(I-A)$ is invertible?
negative_passages.docid: 81618
negative_passages.text: Prove $||a|-|b| | \leq |a-b|$
negative_passages.docid: 21737
negative_passages.text: If $A|B$ and $B|A$ then prove $A=\pm B$
negative_passages.docid: 127296
negative_passages.text: prove that a|b and b|a iff a=+-b
negative_passages.docid: 144266
negative_passages.text: set theory proof of $A\cap B = A \setminus(A\setminus B)$