$\{x: 2x^2\cos(1/x) \le 1\} \cup \{0\}$ is complete.
134601
whether they are complete metric space
37158
upper limit of $\cos (x^2)-\cos (x+1)^2$ is $2$
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
66293
$der(\{x\})$ is closed and $x\in der(der(A))$
156597
Proving a reduction formula for the antiderivative of $\cos^n(x)$
128894
About compactness and completeness of set $X = \mathbb{R}$ with the metric $d(x, y) = \frac{|x-y|}{1+|x-y|}$
16749
Let $A_i= \left \{...,-2,-1,0,1,...,i \right\}$. Find $\bigcup_{i=1}^{n} A_i$ and $\bigcap_{i=1}^{n} A_i$
52787
If $\bigcup F = A$ then $A\in F$ then prove that $A$ has exactly one element
39082
Proving $x^\alpha-\alpha x \le 1- \alpha $
143674
Space of bounded functions is complete
16550
Is $ d(X) \le s(X)? $
74684
$\lim_{x \to 0} {1-x\cot x\over x^2}$
45642
Prove that the Extension Theorem is Complete.
26302
Prove that $(X \cap Y) \cup Z = (X \cup Z) \cap (Y \cup Z)$
142513
Prove that $2xy\mid x^2+y^2-x$ implies $x$ is a perfect square.
14215
Show that the union $\bigcup A_n$ has empty interior in $X$
76490
Proving that $\cos(\arcsin(x))=\sqrt{1-x^2}$