Skip to main content
Aphyd's user avatar
Aphyd's user avatar
Aphyd's user avatar
Aphyd
  • Member for 5 years, 10 months
  • Last seen more than a week ago
7 votes
1 answer
505 views

Show that $\frac{f(x)}{x}$ is a decreasing function implies that $f(x)$ is subadditive

3 votes
3 answers
66 views

Everyone is pleased by you some of the time

3 votes
1 answer
565 views

Proof that the image of a closed cone under a linear transformation is a closed cone [duplicate]

3 votes
3 answers
109 views

In $\mathbb{R}$ with an arbitrary metric, is it true that $d(x, 0) \leq d(x,y)$ for all $x > 0$, $y < 0$?

3 votes
1 answer
99 views

Is this norm equivalent to the $\ell_1$ norm?

3 votes
0 answers
31 views

An equicontinuous sequence of functions bounded by a function $\phi$ with $\lim_{x\rightarrow\pm\infty}\phi(x)$ has a uniformly convergent subsequence

2 votes
2 answers
145 views

Proof that the pointwise limit of this sequence of functions attains its supremum

2 votes
1 answer
191 views

Using ${\rm Lip}1$ to show that $C[0,1]$ is separable

2 votes
1 answer
341 views

What is the P(A|A) if P(A) = 0?

2 votes
1 answer
492 views

Constructive proof that $\liminf na_n = 0$ if the series $\sum_{n=1}^{\infty} a_n$ converges

2 votes
2 answers
433 views

Can someone help me understand Curry's paradox?

2 votes
4 answers
324 views

Prove that a function from a compact interval in R to itself has at least one fixed point without the intermediate value theorem.

2 votes
2 answers
202 views

Is it possible for a Cauchy sequence to have no limit point at all?

1 vote
2 answers
685 views

Prove that every absolutely summable series in L1 is summable

1 vote
0 answers
56 views

Proving this set is compact [duplicate]

1 vote
1 answer
193 views

Show that the sum of two uniformly continuous functions is uniformly continuous in an arbitrary metric space

1 vote
1 answer
116 views

Let $f(x) = \sum_{r_n < x} 2^{-n}$, where $(r_n)$ is an enumeration of $\mathbb{Q}$. Why is $f$ discontinuous everywhere in $[0, 1]$?

1 vote
3 answers
121 views

Define $f : L^2 \rightarrow \mathbb{R}$ by $f(x) = \sum_{n=1}^{\infty} \frac{x_n}{n}$. Is $f$ continuous?

1 vote
1 answer
418 views

Prove that a mapping from a separable space to the Hilbert cube is a homeomorphism

1 vote
1 answer
62 views

If $g(f(x))$ is continuous if and only if $g$ is continuous, then $f$ is a homeomorphism

1 vote
1 answer
118 views

How does Young's inequality reduce to the arithmetic-geometric mean inequality?

1 vote
0 answers
70 views

What functions can have uniformly convergent sequences of derivatives?

1 vote
1 answer
61 views

A fixed point on the space $C([a,b])$

1 vote
0 answers
266 views

Proof that if $(X,d)$ is a metric space and $\forall f:X\to \Bbb R, (f\text{ continuous} \implies f \text{ is bounded})$ then $X$ is compact [duplicate]

1 vote
2 answers
245 views

Proof that this function is not identically zero

0 votes
2 answers
137 views

Constructive proof that the sum of a rational and an irrational is irrational

0 votes
2 answers
1k views

Why must you do polynomial long division to find oblique asymptotes of rational functions?

0 votes
1 answer
63 views

Prove this function is bijective on a domain containing a ball

0 votes
1 answer
80 views

Prove $F_n(x) = \int_0^x f(\sin(nt))dt$ where $f$ is Riemann integrable converges uniformly on $[0,\infty)$

0 votes
1 answer
54 views

Why is the image under integration of a uniformly bounded subset of $C[a,b]$ necessarily compact?