Question

Find a contradiction to: If $t^n < (\sup \{t \in \mathbb{R}_{>0}: t^n < x\})^n$ then $t^n < x$ when this supremum is greater than $x$.

score 95 · Answer 1 · 2026-04-17 09:54:43

Find a contradiction to: If $t^n < (\sup \{t \in \mathbb{R}_{>0}: t^n < x\})^n$ then $t^n < x$ when this supremum is greater than $x$.

score 316 · Answer 2 · 2026-05-10 12:36:41

316

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Compositeness tests for specific classes of generalized repunit numbers

Published on 10 May 2026 - 12:36

score 34 · Answer 3 · 2026-04-16 10:11:07

34

Views

Let $k_i = \{x \in \mathbb N, m\in \mathbb N: x=im\}$ for $i \in \mathbb N$ and $i>1$. Is the $\cap_{i=1}^{\infty} k_i$ empty?

Published on 16 Apr 2026 - 10:11

score 451 · Answer 4 · 2026-04-14 22:22:55

451

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Exercises 1.1.5 Algebraic Topology by Allen Hatcher

Published on 14 Apr 2026 - 22:22

score 232 · Answer 5 · 2026-04-11 18:57:30

232

Views

Example of a multivariable nondifferentiable function with directional derivatives.

Published on 11 Apr 2026 - 18:57

score 258 · Answer 6 · 2026-04-13 10:04:13

258

Views

Continuity counterexamples for probability measures

Published on 13 Apr 2026 - 10:04

score 62 · Answer 7 · 2026-04-12 11:53:48

62

Views

What's an example of a function that is continuous at $0$ but is not second-differentable at $0$?

Published on 12 Apr 2026 - 11:53

score 165 · Answer 8 · 2026-04-30 14:48:00

165

Views

Indeterminate form: $0^0$

Published on 30 Apr 2026 - 14:48

score 96 · Answer 9 · 2026-04-15 11:16:39

96

Views

Why isn't this a counterexample to the division algorithm for polynomials?

Published on 15 Apr 2026 - 11:16

score 1.3k · Answer 10 · 2026-05-10 13:50:19

1.3k

Views

Are my arguments correct about limit points of $A=${$m+n\sqrt 2:m,n\in \mathbb Z$}?

Published on 10 May 2026 - 13:50

score 1.8k · Answer 11 · 2026-04-13 12:55:44

1.8k

Views

If $f$ is continuous and $X$ is locally compact, then $f(X)$ is locally compact.

Published on 13 Apr 2026 - 12:55

score 61 · Answer 12 · 2026-05-10 14:04:05

61

Views

Weak convergence on nonseparable spaces

Published on 10 May 2026 - 14:04

score 499 · Answer 13 · 2026-04-10 18:52:02

499

Views

Counter-example for closed mapping theorem in normed spaces

Published on 10 Apr 2026 - 18:52

score 87 · Answer 14 · 2026-04-16 09:51:20

87

Views

If $f_1, f_2, \dots$ are Riemann integrable and $\sum_n \int |f_n| < \infty$ is $f=\sum_n f_n$ Riemann Integrable?

Published on 16 Apr 2026 - 9:51

score 189 · Answer 15 · 2026-04-16 04:24:24

189

Views

If $E_1 \cup E_2$ is a disjoint union of subsets of $\mathbb{R}^d$, then $m^(E_1 \cup E_2) = m^(E_1) +m^*(E_2)$ may not hold

Published on 16 Apr 2026 - 4:24

List Question

Find a contradiction to: If $t^n < (\sup \{t \in \mathbb{R}_{>0}: t^n < x\})^n$ then $t^n < x$ when this supremum is greater than $x$.

Compositeness tests for specific classes of generalized repunit numbers

Let $k_i = \{x \in \mathbb N, m\in \mathbb N: x=im\}$ for $i \in \mathbb N$ and $i>1$. Is the $\cap_{i=1}^{\infty} k_i$ empty?

Exercises 1.1.5 Algebraic Topology by Allen Hatcher

Example of a multivariable nondifferentiable function with directional derivatives.

Continuity counterexamples for probability measures

What's an example of a function that is continuous at $0$ but is not second-differentable at $0$?

Indeterminate form: $0^0$

Why isn't this a counterexample to the division algorithm for polynomials?

Are my arguments correct about limit points of $A=${$m+n\sqrt 2:m,n\in \mathbb Z$}?

If $f$ is continuous and $X$ is locally compact, then $f(X)$ is locally compact.

Weak convergence on nonseparable spaces

Counter-example for closed mapping theorem in normed spaces

If $f_1, f_2, \dots$ are Riemann integrable and $\sum_n \int |f_n| < \infty$ is $f=\sum_n f_n$ Riemann Integrable?

If $E_1 \cup E_2$ is a disjoint union of subsets of $\mathbb{R}^d$, then $m^(E_1 \cup E_2) = m^(E_1) +m^*(E_2)$ may not hold

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