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Bill
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46 votes
6 answers
4k views

What is the intuition behind Chebyshev's Inequality in Measure Theory

7 votes
3 answers
232 views

if $f(x)\geq0$ for all $x$, then $f+f'+f''+f'''+ \cdots + f^n \geq0$

6 votes
1 answer
301 views

If the image of an operator is closed, is the image of the powers of the operator also closed?

5 votes
3 answers
163 views

How to show that the degree of this field extension is 12?

4 votes
0 answers
134 views

Does irreducible over $\mathbb{R}$ imply irreducible over $\mathbb{Z}$?

4 votes
2 answers
233 views

Spivak's Proof that continuous differentiability implies differentiable

4 votes
1 answer
91 views

How do we use the dominated convergence theorem here? [duplicate]

4 votes
3 answers
335 views

What are the connections between representation theory and differential equations?

3 votes
0 answers
82 views

How to show that the Hilbert-adjoint operator $T^*$ of a (not necessarily bounded) linear operator $T$ on a complex Hilbert space $H$ is bounded

3 votes
1 answer
84 views

How to prove that the delta function is not actually a function

3 votes
1 answer
44 views

Prove if Hilbert dimension is finite, then the Hilbert space as a vector space has the same dimension

3 votes
1 answer
58 views

If $[F(a):F]=n$ and $p(x)$ is of degree $n$ with $a$ as a root, is it the minimal polynomial?

3 votes
2 answers
106 views

In a Banach Algebra, can the product of two elements be invertible if we know one of the element is non invertible?

3 votes
0 answers
66 views

Why does $f$ continuous and its Fourier coefficient converges absolutely implies the Fourier series converges uniformly?

3 votes
3 answers
182 views

if a sequence $x_n$ in a metric space does not contain any convergent subsequence, then $x_n$ is closed in the metric space

3 votes
1 answer
139 views

Do the position and velocity vectors live in the same space?

3 votes
1 answer
112 views

is there a mistake in this proof that union of finite nowhere dense sets is nowhere dense

3 votes
2 answers
129 views

Prove a metric space is totally bounded iff it is bounded in every equivalent metric.

3 votes
2 answers
647 views

Suppose $AB=0$ for some non-zero matrix $B$. Can $A$ be invertible?

3 votes
2 answers
59 views

Is this theorem on product of metric spaces correct?

2 votes
2 answers
90 views

Why is $|x|/x^2=1/|x|$

2 votes
2 answers
52 views

which order do we perform the exponents $x^{2*1/2}$?

2 votes
9 answers
150 views

Find a matrix $A$ with no zero entries such that $A^3=A$

2 votes
2 answers
305 views

Eigenvalues and eigenvectors of a linear transformation that transposes a matrix

2 votes
1 answer
34 views

what triangle inequality was used in this proof that distance between 2 cauchy sequence is cauchy?

2 votes
1 answer
71 views

Is this solutions to Ahlfors 1.1.4 #3 correct, or is there a typo?

2 votes
2 answers
52 views

Prove that $( X,τ)$ is homeomorphic to a subspace of $\Bbb{R}$ if and only if $X$ is countable

2 votes
3 answers
177 views

Is the union of two circles homeomorphic to an interval?

2 votes
2 answers
187 views

when removing a point from a closed set is still a closed set

2 votes
1 answer
55 views

Is $x^2$ differentiable at $0$ if we change the domain to $\{0\}\cup\{\frac1n\mid n\in\mathbb{N}\}$?

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