user avatar
user avatar
user avatar
Nicholas Roberts
  • Member for 7 years, 2 months
  • Last seen this week
  • NY, United States
3 votes

Suppose that $x_n \rightarrow x$ as $ n \rightarrow \infty$. Prove from first principles that if $x_n \leq M$ for all $n$, then $x \leq M$.

3 votes
Accepted

False proof using Nullstellensatz : Let $J = (S)$ an ideal of polynomials then $\sqrt{S} = \sqrt{J}.$ What's wrong?

3 votes
Accepted

Compute $\int_{|z| = r} \frac{|dz|}{|z-a|^2}$ where $|a| \neq r$

2 votes

Why does 'The King Property' of integration work?

2 votes
Accepted

Prove that a convergent sequence with non-negative terms converges to a non-negative limit

1 vote

Induced Map - Correct way to prove function is well-defined

1 vote
Accepted

Consequence of maximum modulus principle

1 vote
Accepted

Convergence of $e^x$

1 vote

Differentiating exponential functions vs differentiating $x^x$

1 vote
Accepted

Is there a condition for $\| T\| =\| T^\ast\|$ where $T$ is a linear operator.

1 vote
Accepted

Prove that $\displaystyle\left|\int_L \frac{z^3}{z^2+1} dz\right| \le \frac{9\pi}{8}$ where $L=\big(z: |z|=3, Re(z) \ge 0\big)$

1 vote
Accepted

Question regarding an equality in a complex integral

1 vote

Induction Proof, $n^2$ is even $\implies$ $n$ is even

1 vote

True or False: Entries on the main diagonal of matrix A

1 vote
Accepted

$\int \frac{\cos x}{x} dx $ using contour integration

1 vote

How can I prove that $\lim_{\varepsilon \to 0} \frac{1}{\operatorname{vol}(B_\varepsilon)} \iiint_{B_\varepsilon} f(x,y,z) \,dV = f(x_0, y_0,z_0)$?

0 votes

Why is the graph of $\sin(y)=x$ different from the graph of $y=\sin^{-1}(x)$?

0 votes
Accepted

Prove $Ab^x$ is injective using $b^x=1$, only when $x = 0$.

0 votes

if $A$ and $B$ are open and $A \cap B = \emptyset$, then $A \cap \overline{B} = \overline{A} \cap B = \emptyset$

0 votes

Product measure, measurable set and integral