query: Show that $ d(x, A) = 0 $ if, and only if, $ x \in \overline{A} $
positive_passages.docid: 151168
positive_passages.text: dist$(x,A)=0$ if and only if $x\in \overline{A}$ (closure of $A$)
negative_passages.docid: 119156
negative_passages.text: $(a,b)=d \overset{?}{\implies} (a^3,b^3)=d^3$
negative_passages.docid: 50019
negative_passages.text: Prove $0$ is a partial limit of $a_n$
negative_passages.docid: 145573
negative_passages.text: How to show that $f$ is a zero function?
negative_passages.docid: 1102
negative_passages.text: Way to determine if X and Y are both over 0
negative_passages.docid: 122076
negative_passages.text: A one line proof that one is zero using Mathematica 10
negative_passages.docid: 16550
negative_passages.text: Is $ d(X) \le s(X)? $
negative_passages.docid: 25874
negative_passages.text: Showing that a certain map is not flat by explicit counterexample
negative_passages.docid: 116382
negative_passages.text: Showing convexity of a function with the restriction over an arbitrary line
negative_passages.docid: 25467
negative_passages.text: Prove that $\lim f(x) =0$ and $\lim (f(2x)-f(x))/x =0$ imply $\lim f(x)/x =0$
negative_passages.docid: 76764
negative_passages.text: Find two closed subsets or real numbers such that $d(A,B)=0$ but $A\cap B=\varnothing$
negative_passages.docid: 125707
negative_passages.text: A simple proof (hopefully) for $2^x \neq 0$
negative_passages.docid: 131876
negative_passages.text: Show that $\int_{a}^{b}{x^{n}f(x)dx}=0$, then $f=0$
negative_passages.docid: 60498
negative_passages.text: Prove that $\lim_{(x,y)\rightarrow(0,0)} \frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}}$ does not exist
negative_passages.docid: 123753
negative_passages.text: In a metric $(X,d)$, prove that for each subset $A$, $x\in\bar{A}$ if and only if $d(x,A)=0.$
negative_passages.docid: 45720
negative_passages.text: Prove that $∂A$ is closed given $∂A = \text{Cl}(A) − \text{Int}(A)$
negative_passages.docid: 30860
negative_passages.text: Prove that $f(x)=0$ in $[-1,1]$.