User Carlyle - Mathematics Stack Exchange

7 votes

$n$ points in the plane can be connected with $n-1$ clockwise, non-intersecting line segments from any starting point

answered Oct 30, 2023 at 21:30

6 votes

Let $A$ be a symmetric $n \times n$ matrix. Prove that $A$ and $A^5$ have the same null space.

answered Dec 21, 2023 at 20:23

5 votes

Accepted

Shadow of a rod

answered May 25, 2022 at 14:39

4 votes

Accepted

Suppose $f=f^{-1}$. Does that imply that $f=id_E$?

answered Nov 22, 2023 at 19:35

4 votes

Accepted

Show that if all sub vectorspace are A-invariant, A must be scaled identity matrix

answered Dec 3, 2023 at 19:24

4 votes

Why pyramid with sharp corners and edges is still a manifold intuitively

answered Sep 25, 2023 at 22:01

3 votes

Is the sequence of functions uniformly convergent in $[0,1)$?

answered Sep 27, 2023 at 22:57

3 votes

Contradiction about the set of all sets

answered Oct 23, 2023 at 20:10

3 votes

continuity (by definition) at a point on piece-wise functions

answered Nov 20, 2023 at 11:09

3 votes

Is there a standard notation for the set of all possible sequences of a set?

answered Dec 21, 2023 at 10:30

3 votes

Accepted

What do you call this kind of metric space?

answered Dec 24, 2023 at 9:55

3 votes

Prove: in geometric sequence ($0\ <\ r\ <\ 1$) the ratio between a term and the sum of all following terms doesn't depend on the location of that term

answered May 21, 2022 at 11:21

3 votes

Accepted

Proof that $\sup \frac{1}{A} = \frac{1}{\inf A}$

answered Jul 19, 2023 at 8:06

3 votes

Accepted

Showing that for all $f: X \to Y$ there exists $S, g: X \to S, h: S \to Y$ with $g$ injective and $h$ surjective such that $f = h \circ g$

answered Sep 20, 2023 at 21:39

3 votes

About infimum of a subgroup of $(\mathbb{R},+)$

answered Sep 23, 2023 at 15:08

3 votes

Accepted

How can I show that these two topologies are the same?

answered Sep 24, 2023 at 18:56

3 votes

Why isn't continuity necessary for existance of partial derivatives?

answered Jun 13 at 9:35

2 votes

I have a proof that the axiom of infinity leads to contradiction, I must be wrong but cannot see why

answered May 30 at 9:56

2 votes

Accepted

Proving $f(x) = \frac{1}{x}$ is not uniformly continuous on (0,1]

answered Dec 29, 2023 at 4:37

2 votes

Accepted

Uniform convergence of $\sum_{m=1}^{\infty} (-1)^m \{{(m+1)^s - m^s} \}$ for $0 < \Re(s) < 1$

answered Jan 6 at 7:56

2 votes

Accepted

Altering the identity axiom in group theory

answered Aug 31, 2023 at 22:02

2 votes

Accepted

A characterization of closure of a certain class of sets in $\mathbb{R}^n$

answered Sep 19, 2023 at 18:53

2 votes

Accepted

Defining an explicit $f:\mathbb{R}\to\mathbb{R}$ whose graph is "extremely scattered" across $\mathbb{R}\times\mathbb{R}$?

answered Aug 1, 2023 at 21:29

2 votes

Accepted

Is every positive integer representable as $N = x^2 + y^2 + z^2 + dw^2, 1 \le d \le 7$ with $x,y,z,w$ as Fibonacci numbers?

answered Jul 19, 2023 at 10:55

2 votes

How do I prove that $\forall a \forall b(\neg a<b\iff b\leq a)$

answered May 25, 2022 at 14:28

2 votes

Can $⟨a_n⟩$ be oscillatory if $\lim_{n\rightarrow\infty}a_{n+1}/a_n = 1$?

answered Jun 3, 2022 at 6:44

2 votes

Intuitively, why does it make sense to go second in dice game to maximize chance of winning?

answered Jul 17, 2022 at 13:52

2 votes

Accepted

Notation for powerset with cardinality condition

answered Nov 20, 2023 at 11:37

2 votes

Accepted

Why can we produce a composition of two functions, if we know that the codomain of the inner function is equal to the domain of the outer function?

answered Nov 21, 2023 at 21:21

2 votes

Metric spaces where each point sees each distance exactly once

answered Dec 16, 2023 at 22:43

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82 Answers

$n$ points in the plane can be connected with $n-1$ clockwise, non-intersecting line segments from any starting point

Let $A$ be a symmetric $n \times n$ matrix. Prove that $A$ and $A^5$ have the same null space.

Shadow of a rod

Suppose $f=f^{-1}$. Does that imply that $f=id_E$?

Show that if all sub vectorspace are A-invariant, A must be scaled identity matrix

Why pyramid with sharp corners and edges is still a manifold intuitively

Is the sequence of functions uniformly convergent in $[0,1)$?

Contradiction about the set of all sets

continuity (by definition) at a point on piece-wise functions

Is there a standard notation for the set of all possible sequences of a set?

What do you call this kind of metric space?

Prove: in geometric sequence ($0\ <\ r\ <\ 1$) the ratio between a term and the sum of all following terms doesn't depend on the location of that term

Proof that $\sup \frac{1}{A} = \frac{1}{\inf A}$

Showing that for all $f: X \to Y$ there exists $S, g: X \to S, h: S \to Y$ with $g$ injective and $h$ surjective such that $f = h \circ g$

About infimum of a subgroup of $(\mathbb{R},+)$

How can I show that these two topologies are the same?

Why isn't continuity necessary for existance of partial derivatives?

I have a proof that the axiom of infinity leads to contradiction, I must be wrong but cannot see why

Proving $f(x) = \frac{1}{x}$ is not uniformly continuous on (0,1]

Uniform convergence of $\sum_{m=1}^{\infty} (-1)^m \{{(m+1)^s - m^s} \}$ for $0 < \Re(s) < 1$

Altering the identity axiom in group theory

A characterization of closure of a certain class of sets in $\mathbb{R}^n$

Defining an explicit $f:\mathbb{R}\to\mathbb{R}$ whose graph is "extremely scattered" across $\mathbb{R}\times\mathbb{R}$?

Is every positive integer representable as $N = x^2 + y^2 + z^2 + dw^2, 1 \le d \le 7$ with $x,y,z,w$ as Fibonacci numbers?

How do I prove that $\forall a \forall b(\neg a<b\iff b\leq a)$

Can $⟨a_n⟩$ be oscillatory if $\lim_{n\rightarrow\infty}a_{n+1}/a_n = 1$?

Intuitively, why does it make sense to go second in dice game to maximize chance of winning?

Notation for powerset with cardinality condition

Why can we produce a composition of two functions, if we know that the codomain of the inner function is equal to the domain of the outer function?

Metric spaces where each point sees each distance exactly once