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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?

Are categories larger than classes?

What system was Grothendieck working in when he introduced universes?

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

Terry Tao's computational perspective on set theory

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?

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

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

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

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

Proving that the cross ratio is a Möbius transformation

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

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

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

Oriented atlas on a circle

Why is $f(U) \cap V$ the zero set of $y^{n+1}, \dots, y^m$? [duplicate]

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

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

There exists no inner product on $\mathbb R^n$ that induces the maximum norm

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

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

Finding a subfield of $\mathbb R$ such that $e^2$ is of degree five over that subfield.

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