User user18921 - Mathematics Stack Exchange

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	3,400 reputation	bio	website		visits	member for	8 months
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3

20

votes

4

answers

376

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Is $\mathbb{N}$ impossible to pin down?

may 9 at 17:11 Carl Mummert 25.6k

5

18

votes

6

answers

463

views

Struggling with “technique-based” mathematics, can people relate to this? And what, if anything, can be done about it?

soft-question

mar 3 at 5:44 Kaz 2,162

3

16

votes

5

answers

400

views

Why hasn't GCH become a standard axiom of ZFC?

set-theory cardinals axioms

mar 31 at 7:39 Arthur Fischer♦ 21.3k

1

15

votes

1

answer

160

views

Non-associative version of a group satisfying these identities: $(xy)y^{-1}=y^{-1}(yx)=x$

abstract-algebra

may 17 at 13:15 Jack Schmidt 20.1k

4

14

votes

3

answers

384

views

What is dual to “There exists unique?”

logic quantifiers

may 13 at 3:55 Dan Christensen 1,565

1

12

votes

5

answers

319

views

Can an algebraic structure have indistinguishable elements?

abstract-algebra

20h ago user18921 3,400

3

12

votes

0

answers

155

views

Is there an axiomatic approach to ordinal arithmetic?

reference-request ordinals axioms

apr 16 at 8:25 mezhang 1,403

2

11

votes

2

answers

166

views

Is second order logic even a logic?

logic higher-order-logic

may 14 at 0:10 Alex Kocurek 663

4

10

votes

1

answer

219

views

What of the “Sets, Classes, and Categories” approach to the foundations?

set-theory category-theory foundations

apr 23 at 23:20 Damien L 3,501

2

10

votes

3

answers

311

views

When we say, “ZFC can found most of mathematics,” what do we really mean?

logic set-theory foundations

feb 27 at 10:00 user18921 3,400

3

9

votes

6

answers

229

views

Should every group be a monoid, or should no group be a monoid?

abstract-algebra soft-question terminology

may 15 at 7:11 Thomas Klimpel 1,784

3

9

votes

2

answers

197

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Does there exist another way of obtaining a topological space from a metric space equally deserving of the term “canonical”?

general-topology soft-question category-theory metric-spaces

jan 31 at 1:15 Martin Brandenburg 22.5k

3

8

votes

2

answers

125

views

How many ordinals can we cram into $\mathbb{R}_+$, respecting order?

order-theory ordinals

apr 2 at 15:22 Henning Makholm 53.6k

8

votes

2

answers

262

views

How many paths exist between two points in the plane?

general-topology elementary-set-theory

mar 30 at 15:54 Asaf Karagila 90.8k

7

votes

1

answer

72

views

What's more robust than a structural homomorphisms?

category-theory model-theory

may 17 at 15:11 user18921 3,400

1

7

votes

1

answer

82

views

Is there a name for relations with this property?

graph-theory terminology relations equivalence-relations

may 14 at 12:33 user18921 3,400

7

votes

5

answers

186

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Why are homomorphisms usually assumed to be functions?

soft-question

may 1 at 0:36 Andreas Blass 7,068

7

votes

2

answers

143

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Assuming Freiling's axiom of symmetry, can we define a specific set $X \subseteq \mathbb{R}$ such that $|\mathbb{N}|<|X|<|\mathbb{R}|$?

set-theory

apr 30 at 6:52 Asaf Karagila 90.8k

2

7

votes

2

answers

101

views

The category Set seems more prominent/important than the category Rel. Why is this?

soft-question category-theory

apr 8 at 22:34 Omar 1,360

7

votes

2

answers

102

views

What is the relationship between completeness and local compactness?

general-topology soft-question

apr 6 at 18:08 Byron Schmuland 15.4k

4

7

votes

3

answers

74

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Which properties are inherited by the Cartesian product of two sets equipped with a binary operation?

abstract-algebra magma

mar 14 at 13:06 Tara B 4,088

1

7

votes

1

answer

139

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Why not just study the consequences of Hausdorff axiom? What do statements like, “The arbitrary union of open sets is open,” gain us?

general-topology

mar 5 at 10:33 user18921 3,400

1

7

votes

1

answer

124

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Does non-standard analysis still make use of classical topology?

real-analysis general-topology nonstandard-analysis

feb 16 at 3:26 Ittay Weiss 18.9k

1

7

votes

1

answer

215

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Is it possible to avoid redundancy in a foundational work?

soft-question set-theory

feb 2 at 1:27 Asaf Karagila 90.8k

2

6

votes

0

answers

70

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Working with subsets, as opposed to elements.

soft-question notation

may 17 at 6:31 user18921 3,400

1

6

votes

3

answers

169

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If a topological space is a path-connected, it is also connected. The converse fails. Can this be remedied?

general-topology connectedness

apr 17 at 5:53 user18921 3,400

3

6

votes

0

answers

67

views

Accessible introduction to category theory from the point of view of preorders. [duplicate]

reference-request soft-question category-theory

apr 11 at 8:16 user18921 3,400

1

6

votes

2

answers

92

views

Is a topological space a structure?

category-theory model-theory

apr 8 at 7:39 Zhen Lin 20.9k

6

votes

2

answers

84

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Is there a way to axiomatize the category of sets and relations?

category-theory axioms foundations

apr 2 at 4:20 Hurkyl 21.5k

1

6

votes

1

answer

216

views

Is there a rigorous theory of context, whereby sets can gain additional structure within a context?

abstract-algebra reference-request soft-question notation

mar 29 at 20:20 user18921 3,400

user18921

181 Questions