query: Show that $a$ is minimum
positive_passages.docid: 146421
positive_passages.text: How to prove a total order has a unique minimal element
negative_passages.docid: 42266
negative_passages.text: Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
negative_passages.docid: 77855
negative_passages.text: Prove that if $A$ has a maximum, then the maximum must be the supremum
negative_passages.docid: 65827
negative_passages.text: When $\min_{x \in X,y \in Y} f(x,y) = \min_{x \in X} \min_{y \in Y} f(x,y)$?
negative_passages.docid: 20055
negative_passages.text: Find minimum value of $\sum \frac{\sqrt{a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}$
negative_passages.docid: 47820
negative_passages.text: How can I show a supremum of a set is also its limit point?
negative_passages.docid: 86518
negative_passages.text: Does $X$ have a lower bound?
negative_passages.docid: 63124
negative_passages.text: Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
negative_passages.docid: 53112
negative_passages.text: Proving using AM-GM inequality
negative_passages.docid: 55461
negative_passages.text: How to prove that if $a$ belongs to $\mathbb R$, such that $0\leq a \leq\epsilon$, then $a = 0$
negative_passages.docid: 77192
negative_passages.text: How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?
negative_passages.docid: 93076
negative_passages.text: When $\min \max = \max \min$?
negative_passages.docid: 126259
negative_passages.text: Minimum of a function on an open interval
negative_passages.docid: 24221
negative_passages.text: Complex numbers - minimum value proof
negative_passages.docid: 106979
negative_passages.text: Prove the inequality and limitation
negative_passages.docid: 15969
negative_passages.text: How to prove that $A$ is positive semi-definite if all principal minors are non-negative?
negative_passages.docid: 96382
negative_passages.text: Minimum of the Gamma Function $\Gamma (x)$ for $x>0$. How to find $x_{\min}$?