User justin

58 votes

10 answers

6k views

Is it an abuse of language to say "the integers," "the rational numbers," or "the real numbers," etc.?

asked Jun 9, 2016 at 14:28

38 votes

7 answers

4k views

Do the axioms of set theory actually define the notion of a set?

logic soft-question set-theory model-theory

asked May 18, 2016 at 5:39

31 votes

9 answers

4k views

Is formal truth in mathematical logic a generalization of everyday, intuitive truth?

logic soft-question philosophy foundations formal-systems

asked May 12, 2016 at 1:47

17 votes

3 answers

2k views

Should this "definition" of set equality be an axiom?

logic axioms foundations

asked Apr 2, 2017 at 22:25

12 votes

2 answers

1k views

How to prove that Gödel's Incompleteness Theorems apply to ZFC?

logic set-theory predicate-logic first-order-logic incompleteness

asked Jan 4, 2015 at 5:24

11 votes

3 answers

1k views

Is the "domain of discourse" in axiomatic set theory also a "set"?

logic set-theory predicate-logic axioms

asked Dec 31, 2014 at 20:46

11 votes

2 answers

2k views

Is it circular to define the Von Neumann universe using "sets"?

set-theory model-theory philosophy foundations

asked May 27, 2016 at 20:48

11 votes

1 answer

2k views

Are categories larger than classes?

category-theory set-theory definition

asked Mar 31, 2016 at 22:36

9 votes

2 answers

2k views

Terry Tao's computational perspective on set theory

soft-question set-theory foundations

asked Jun 1, 2016 at 19:24

8 votes

0 answers

275 views

What system was Grothendieck working in when he introduced universes?

logic reference-request set-theory math-history

asked Apr 16, 2018 at 2:42

7 votes

0 answers

124 views

Does introducing a new type create a different extension, and is it still conservative?

logic set-theory axioms foundations formal-systems

asked Jun 15, 2017 at 21:49

7 votes

1 answer

185 views

Do mathematical objects have underlying types?

logic soft-question definition

asked Jan 27, 2016 at 18:47

6 votes

3 answers

367 views

Confusion in proof that primes $p = 4k + 1$ are uniquely the sums of two squares

number-theory elementary-number-theory prime-numbers

asked Dec 5, 2013 at 3:43

6 votes

3 answers

3k views

Eigenvalues of a Permutation?

linear-algebra eigenvalues-eigenvectors

asked Dec 8, 2013 at 21:18

5 votes

1 answer

1k views

Left-invariant vector fields on the circle $S^1$

differential-geometry manifolds lie-groups smooth-manifolds

asked Apr 21, 2016 at 21:44

4 votes

2 answers

426 views

The difference between a finite set and an ordered $n-$tuple? Proving the set of all finite subsets of a countable set is countable.

general-topology elementary-set-theory

asked Jan 18, 2014 at 19:31

4 votes

4 answers

874 views

Do these theorems about power sets hold for the empty set?

general-topology elementary-set-theory

asked Jan 19, 2014 at 2:58

4 votes

3 answers

3k views

Proving that cardinality of the reals = cardinality of $[0,1]$

general-topology elementary-set-theory

asked Feb 2, 2014 at 17:58

4 votes

1 answer

787 views

Is every isomorphism of an algebraically closed field onto one of its subfields an automorphism?

abstract-algebra field-theory extension-field

asked Apr 4, 2015 at 21:01

4 votes

1 answer

505 views

Smooth function on a manifold not dependent on coordinate chart

differential-geometry manifolds smooth-manifolds

asked Feb 23, 2016 at 1:34

4 votes

1 answer

223 views

Proving that extension by radicals implies solvable group

abstract-algebra galois-theory

asked Apr 24, 2015 at 4:36

4 votes

2 answers

326 views

If $\overline A\cap B = A\cap \overline B = \varnothing$, $A\cup B$ is disconnected.

general-topology metric-spaces

asked May 21, 2015 at 1:50

4 votes

1 answer

673 views

In $\mathbb Q_p$, proving every open ball is the disjoint union of more than one open ball

general-topology metric-spaces p-adic-number-theory

asked May 23, 2015 at 20:53

4 votes

2 answers

1k views

Proving that the cross ratio is a Möbius transformation

complex-analysis mobius-transformation

asked Jun 28, 2015 at 3:34

4 votes

1 answer

315 views

Why do we write $df/dx$ instead of $df/dx(x)$?

derivatives notation

asked Aug 30, 2015 at 17:52

3 votes

1 answer

1k views

Pronouncing the symbols $\oplus,\otimes,\rtimes,\cup$, and $\cap$. [closed]

abstract-algebra notation pronunciation

asked Nov 5, 2015 at 21:33

3 votes

2 answers

2k views

Smooth functions between manifolds and subsets of manifolds

differential-geometry manifolds smooth-manifolds

asked Feb 25, 2016 at 1:24

3 votes

2 answers

11k views

Find all irreducible monic polynomials of degree 3 in $\mathbb Z/3\mathbb Z[x].$

abstract-algebra

asked Dec 4, 2014 at 5:05

3 votes

1 answer

81 views

Prove there is a basis of $V$ w.r.t. which $T$ is the companion matrix of $a(x)$

linear-algebra abstract-algebra modules companion-matrices

asked Dec 8, 2015 at 16:49

3 votes

1 answer

78 views

If $F\cong R^n$, why is $1\otimes \psi\colon F\otimes_R L\to F\otimes_R M$ injective?

modules flatness

asked Dec 15, 2015 at 2:09

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108 Questions

Is it an abuse of language to say "the integers," "the rational numbers," or "the real numbers," etc.?

Do the axioms of set theory actually define the notion of a set?

Is formal truth in mathematical logic a generalization of everyday, intuitive truth?

Should this "definition" of set equality be an axiom?

How to prove that Gödel's Incompleteness Theorems apply to ZFC?

Is the "domain of discourse" in axiomatic set theory also a "set"?

Is it circular to define the Von Neumann universe using "sets"?

Are categories larger than classes?

Terry Tao's computational perspective on set theory

What system was Grothendieck working in when he introduced universes?

Does introducing a new type create a different extension, and is it still conservative?

Do mathematical objects have underlying types?

Confusion in proof that primes $p = 4k + 1$ are uniquely the sums of two squares

Eigenvalues of a Permutation?

Left-invariant vector fields on the circle $S^1$

The difference between a finite set and an ordered $n-$tuple? Proving the set of all finite subsets of a countable set is countable.

Do these theorems about power sets hold for the empty set?

Proving that cardinality of the reals = cardinality of $[0,1]$

Is every isomorphism of an algebraically closed field onto one of its subfields an automorphism?

Smooth function on a manifold not dependent on coordinate chart

Proving that extension by radicals implies solvable group

If $\overline A\cap B = A\cap \overline B = \varnothing$, $A\cup B$ is disconnected.

In $\mathbb Q_p$, proving every open ball is the disjoint union of more than one open ball

Proving that the cross ratio is a Möbius transformation

Why do we write $df/dx$ instead of $df/dx(x)$?

Pronouncing the symbols $\oplus,\otimes,\rtimes,\cup$, and $\cap$. [closed]

Smooth functions between manifolds and subsets of manifolds

Find all irreducible monic polynomials of degree 3 in $\mathbb Z/3\mathbb Z[x].$

Prove there is a basis of $V$ w.r.t. which $T$ is the companion matrix of $a(x)$

If $F\cong R^n$, why is $1\otimes \psi\colon F\otimes_R L\to F\otimes_R M$ injective?