User tomasz

107 votes

Why is radian so common in maths?

geometry education

answered May 24, 2016 at 8:48

51 votes

Are there mathematical concepts that exist in dimension $4$, but not in dimension $3$?

answered Sep 5, 2019 at 0:37

42 votes

Difference between closed, bounded and compact sets

general-topology metric-spaces compactness

answered Feb 13, 2014 at 11:30

37 votes

Accepted

Is there an example of an ordered ring that is not isomorphic to any subring of the real numbers?

abstract-algebra ring-theory order-theory

answered Apr 5, 2017 at 17:30

33 votes

Accepted

Is it necessary for one to understand analysis?

analysis soft-question learning

answered Apr 7, 2015 at 13:42

31 votes

Accepted

How to show $i^{-1} = -i$?

complex-numbers

answered Feb 19, 2014 at 21:10

31 votes

How to learn from proofs?

soft-question

answered Jul 7, 2012 at 13:07

29 votes

On "familiarity" (or How to avoid "going down the Math Rabbit Hole"?)

soft-question self-learning

answered Dec 25, 2013 at 0:09

27 votes

Accepted

Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed

general-topology

answered Oct 26, 2012 at 23:27

23 votes

The Euler characteristic of S1: a paradox

general-topology

answered Aug 14, 2012 at 23:29

23 votes

Are the only sets in $\mathbb{R^1}$ which are both open and closed $\mathbb{R^1}$ and $\emptyset$?

general-topology

answered Sep 23, 2012 at 11:32

21 votes

Visualizing quotient groups: $\mathbb{R/Q}$

group-theory topological-groups visualization

answered Aug 14, 2012 at 0:26

19 votes

Accepted

Example when the torsion of a module is not a submodule.

abstract-algebra modules

answered Nov 21, 2013 at 4:49

19 votes

Galois Field GF(4)

field-theory finite-fields

answered Jul 19, 2012 at 20:14

18 votes

If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.

abstract-algebra ring-theory

answered Jul 26, 2012 at 15:32

17 votes

Accepted

Does the union of two not disjoint open balls always contain the line connecting the two centers?

geometry functional-analysis hilbert-spaces banach-spaces

answered Aug 20, 2016 at 11:43

16 votes

Accepted

Is there an uncountable proper sub-field of $\mathbf{R}$?

abstract-algebra field-theory

answered Dec 23, 2013 at 2:12

16 votes

Why do we use trig functions in Fourier transforms, and not other periodic functions?

fourier-analysis fourier-series fourier-transform harmonic-analysis periodic-functions

answered Apr 12, 2018 at 14:38

15 votes

Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?

real-analysis general-topology compactness

answered May 31, 2016 at 19:38

15 votes

How to construct a Bernstein set and what are their applications?

real-analysis general-topology descriptive-set-theory

answered Jul 12, 2012 at 1:59

14 votes

Accepted

What is the motivation for differential forms?

differential-geometry multivariable-calculus soft-question differential-forms

answered Jul 23, 2013 at 4:13

14 votes

subset of binary space countable?

sequences-and-series general-topology functions elementary-set-theory

answered Feb 25, 2016 at 7:59

13 votes

Accepted

How to think of the field $F(\alpha)$

abstract-algebra field-theory

answered Jul 9, 2012 at 20:03

12 votes

Accepted

Topological manifolds (dimension)

general-topology manifolds dimension-theory-analysis

answered May 19, 2013 at 20:45

11 votes

Accepted

Why metrizable group requires continuity of inverse?

real-analysis abstract-algebra general-topology group-theory topological-groups

answered May 31, 2012 at 4:29

11 votes

Accepted

Every point closed $\stackrel{?}{\Rightarrow}$ space is Hausdorff

general-topology

answered Sep 3, 2012 at 20:43

10 votes

Accepted

Infinitely many axioms of ZFC vs. finitely many axioms of NBG

logic soft-question set-theory first-order-logic philosophy

answered Dec 18, 2021 at 12:37

10 votes

What does $C^{\infty}_0$ stand for

functional-analysis analysis notation

answered Jan 19, 2015 at 20:58

10 votes

What is an irreducible character of a finite group?

group-theory finite-groups representation-theory characters

answered Aug 25, 2012 at 18:01

10 votes

Accepted

Why do mathematicians use this symbol $\mathbb R$ to represent the real numbers?

abstract-algebra soft-question notation

answered Oct 19, 2012 at 19:15

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959 Answers

Why is radian so common in maths?

Are there mathematical concepts that exist in dimension $4$, but not in dimension $3$?

Difference between closed, bounded and compact sets

Is there an example of an ordered ring that is not isomorphic to any subring of the real numbers?

Is it necessary for one to understand analysis?

How to show $i^{-1} = -i$?

How to learn from proofs?

On "familiarity" (or How to avoid "going down the Math Rabbit Hole"?)

Showing that projections $\mathbb{R}^2 \to \mathbb{R}$ are not closed

The Euler characteristic of S1: a paradox

Are the only sets in $\mathbb{R^1}$ which are both open and closed $\mathbb{R^1}$ and $\emptyset$?

Visualizing quotient groups: $\mathbb{R/Q}$

Example when the torsion of a module is not a submodule.

Galois Field GF(4)

If $f: \mathbb Q\to \mathbb Q$ is a homomorphism, prove that $f(x)=0$ for all $x\in\mathbb Q$ or $f(x)=x$ for all $x$ in $\mathbb Q$.

Does the union of two not disjoint open balls always contain the line connecting the two centers?

Is there an uncountable proper sub-field of $\mathbf{R}$?

Why do we use trig functions in Fourier transforms, and not other periodic functions?

Is $[0,1] \cap \Bbb Q$ a compact subset of $\Bbb Q$?

How to construct a Bernstein set and what are their applications?

What is the motivation for differential forms?

subset of binary space countable?

How to think of the field $F(\alpha)$

Topological manifolds (dimension)

Why metrizable group requires continuity of inverse?

Every point closed $\stackrel{?}{\Rightarrow}$ space is Hausdorff

Infinitely many axioms of ZFC vs. finitely many axioms of NBG

What does $C^{\infty}_0$ stand for

What is an irreducible character of a finite group?

Why do mathematicians use this symbol $\mathbb R$ to represent the real numbers?