Question

Is there a "global" convexity locally around a minimum?

score 259 · Answer 1 · 2026-04-20 11:40:35

259

Views

Is there a "global" convexity locally around a minimum?

Published on 20 Apr 2026 - 11:40

score 505 · Answer 2 · 2026-04-14 12:02:43

505

Views

Prove that Monotone Convergence Theorem implies Nested Interval Property without using Axiom of Completeness.

Published on 14 Apr 2026 - 12:02

score 143 · Answer 3 · 2026-04-11 03:40:09

143

Views

Defined, and Limit Existence True or False Explanation

Published on 11 Apr 2026 - 3:40

score 28 · Answer 4 · 2026-04-19 22:20:45

28

Views

A bounded function on $[a,b]$ that is continuous except finitely many points is measurable (proof verification)

Published on 19 Apr 2026 - 22:20

score 53 · Answer 5 · 2026-03-27 21:05:42

53

Views

Determine if a $4$-th root of unity is contained in $\mathbb{F}_9$

Published on 27 Mar 2026 - 21:05

score 470 · Answer 6 · 2026-04-16 04:31:56

470

Views

Suppose $a$, $b$, $c$, and $d$ are real numbers, $0<a<b$, and $d>0$. Prove that if $ac\geq bd$ then $c>d$.

Published on 16 Apr 2026 - 4:31

score 198 · Answer 7 · 2026-04-14 01:04:58

198

Views

Simplifying Axler's proof that every operator on an odd-dimensional real vector space has an eigenvalue (linear algebra done right, 2nd ed)

Published on 14 Apr 2026 - 1:04

score 27 · Answer 8 · 2026-04-14 21:36:06

27

Views

If $x<y$ then $\exists\, M \in \mathbb{N}$ such that $\frac{1}{n}<y-x\;\forall\; n>M$

Published on 14 Apr 2026 - 21:36

score 1.5k · Answer 9 · 2026-03-25 13:51:07

1.5k

Views

Proof that indicator function is random variable (Borel-measurable)

Published on 25 Mar 2026 - 13:51

score 69 · Answer 10 · 2026-04-16 02:41:04

69

Views

Prove that for all sets $A$ and $B$, $( A \cup B ) - B = A$ implies $A \cap B =\varnothing$.

Published on 16 Apr 2026 - 2:41

score 97 · Answer 11 · 2026-04-11 11:55:47

97

Views

Integral and sum function

Published on 11 Apr 2026 - 11:55

score 65 · Answer 12 · 2026-04-16 21:40:48

65

Views

Integrability of $f(x,y)=(1-x)^{a}$ on $D=\{(x,y):0<x^2+y^2<1\}$

Published on 16 Apr 2026 - 21:40

score 210 · Answer 13 · 2026-04-15 20:21:35

To disprove a statement of the form $\exists x \forall y (x = ...y...)$, can I negate like this: $\forall x \exists y \lnot(x = ...y...)$?

score 99 · Answer 14 · 2026-04-13 20:15:23

99

Views

Well-ordering theorem through repetitive use of the Axiom of Choice

Published on 13 Apr 2026 - 20:15

score 861 · Answer 15 · 2026-04-16 00:01:47

861

Views

Show that the inequality $|f(x)-f(y)| \leq M||x-y||+\epsilon$.

Published on 16 Apr 2026 - 0:01

List Question

Is there a "global" convexity locally around a minimum?

Prove that Monotone Convergence Theorem implies Nested Interval Property without using Axiom of Completeness.

Defined, and Limit Existence True or False Explanation

A bounded function on $[a,b]$ that is continuous except finitely many points is measurable (proof verification)

Determine if a $4$-th root of unity is contained in $\mathbb{F}_9$

Suppose $a$, $b$, $c$, and $d$ are real numbers, $0<a<b$, and $d>0$. Prove that if $ac\geq bd$ then $c>d$.

Simplifying Axler's proof that every operator on an odd-dimensional real vector space has an eigenvalue (linear algebra done right, 2nd ed)

If $x<y$ then $\exists\, M \in \mathbb{N}$ such that $\frac{1}{n}<y-x\;\forall\; n>M$

Proof that indicator function is random variable (Borel-measurable)

Prove that for all sets $A$ and $B$, $( A \cup B ) - B = A$ implies $A \cap B =\varnothing$.

Integral and sum function

Integrability of $f(x,y)=(1-x)^{a}$ on $D=\{(x,y):0<x^2+y^2<1\}$

To disprove a statement of the form $\exists x \forall y (x = ...y...)$, can I negate like this: $\forall x \exists y \lnot(x = ...y...)$?

Well-ordering theorem through repetitive use of the Axiom of Choice

Show that the inequality $|f(x)-f(y)| \leq M||x-y||+\epsilon$.

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