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 92 · Answer 1 · 2018-02-16 20:44:07

92

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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 $x$.

Published on 16 Feb 2018 - 20:44

score 311 · Answer 2 · 2026-03-25 04:16:14

311

Views

Compositeness tests for specific classes of generalized repunit numbers

Published on 25 Mar 2026 - 4:16

score 31 · Answer 3 · 2018-02-18 19:32:55

31

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 18 Feb 2018 - 19:32

score 448 · Answer 4 · 2026-03-17 20:02:49

448

Views

Exercises 1.1.5 Algebraic Topology by Allen Hatcher

Published on 17 Mar 2026 - 20:02

score 230 · Answer 5 · 2026-03-25 03:34:34

230

Views

Example of a multivariable nondifferentiable function with directional derivatives.

Published on 25 Mar 2026 - 3:34

score 255 · Answer 6 · 2018-02-21 00:50:26

255

Views

Continuity counterexamples for probability measures

Published on 21 Feb 2018 - 0:50

score 59 · Answer 7 · 2018-02-21 09:16:33

59

Views

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

Published on 21 Feb 2018 - 9:16

score 160 · Answer 8 · 2018-02-21 09:35:27

160

Views

Indeterminate form: $0^0$

Published on 21 Feb 2018 - 9:35

score 93 · Answer 9 · 2018-02-22 01:42:02

93

Views

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

Published on 22 Feb 2018 - 1:42

score 1.3k · Answer 10 · 2026-03-25 01:17:42

1.3k

Views

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

Published on 25 Mar 2026 - 1:17

score 1.8k · Answer 11 · 2018-02-24 00:57:26

1.8k

Views

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

Published on 24 Feb 2018 - 0:57

score 58 · Answer 12 · 2026-03-25 09:31:26

58

Views

Weak convergence on nonseparable spaces

Published on 25 Mar 2026 - 9:31

score 497 · Answer 13 · 2026-03-25 11:12:42

497

Views

Counter-example for closed mapping theorem in normed spaces

Published on 25 Mar 2026 - 11:12

score 84 · Answer 14 · 2018-02-28 16:14:39

84

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 28 Feb 2018 - 16:14

score 186 · Answer 15 · 2018-02-28 18:35:01

186

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 28 Feb 2018 - 18:35

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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