Let E = $\{x\in \mathbb{Q}: x>0$ and $x^2 <2\}$. Prove E does not have a largest element.
67161
No maximum(minimum) of rationals whose square is lesser(greater) than $2$.
118195
How does one prove that $e$ exists?
80202
Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?
113411
If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
108550
Elements of $\mathbb Q(2^{1/3})$
14215
Show that the union $\bigcup A_n$ has empty interior in $X$
147705
Show that $\mathbb{E}(T) = \sum\limits^\infty_{k=1}\mathbb{P}(T \geq k)$ for $T$ nonnegative integer valued and $E[T] < \infty$
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
88690
$\int_a^b f(x)\mathrm dx=0$ for all $-\infty<a<b<\infty$ a,b rational implies $f=0$ a.e
109109
Show that $E(XE[X|G])=E[(E[X|G)^2]$
23946
Prove the definitions of $e$ to be equivalent
114729
If $E$ has measure zero, then does $E^2$ have measure zero?
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
155232
Prove that inequality is true for $x>0$: $(e^x-1)\ln(1+x) > x^2$
23712
$F$ is a finite field of size $s$. Prove that if $s=2^m$ for some $m>0$, then all elements of F have a square root.