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The ring of integers of a number field is finitely generated.
commutative-algebra
algebraic-number-theory
alternative-proof
Is my proof correct for: $\sqrt[7]{7!} < \sqrt[8]{8!}$
algebra-precalculus
proof-verification
alternative-proof
How to show that $\lim_{n\to \infty} \frac{a_1 +a_2 + \cdots + a_n}{n} = 0?$ [duplicate]
real-analysis
sequences-and-series
limits
solution-verification
alternative-proof
Abel-Ruffini theorem, Galois theory and minima and maxima
polynomials
galois-theory
alternative-proof
radicals
A Question on Epsilon-Delta Proofs in Measure Theory
measure-theory
proof-explanation
lp-spaces
alternative-proof
epsilon-delta
Prove that there is no smallest positive real number
proof-verification
proof-writing
alternative-proof
Elegant solution to $\lim\limits_{n \to \infty}{[n(\sqrt[n]{a} - 1)]}$
calculus
real-analysis
limits
alternative-proof
If $a_0+\frac{a_1}{2}+\dots + \frac{a_n}{n+1}=0$ then $a_nx^n+\dots + a_0$ has a root in $[0,1]$ [duplicate]
polynomials
proof-verification
contest-math
roots
alternative-proof
How to prove that $\lim\limits_{x\to0}\frac{\tan x}x=1$?
calculus
limits
trigonometry
derivatives
alternative-proof
Is there a way to prove $\pi$ is irrational using any of its infinite series?
alternative-proof
irrational-numbers
A very interesting question: intersection point of $x^y=y^x$
calculus
limits
exponential-function
alternative-proof
exponential-diophantine-equations
What is $x$ if $x^{x^x} = {(1/2)}^{\sqrt 2}$?
algebra-precalculus
exponential-function
alternative-proof
Direct combinatorial proof of a sum identity on formal Lagrange polynomials
abstract-algebra
combinatorics
polynomials
alternative-proof
Prob. 2(b), Sec. 25, in Munkres' TOPOLOGY, 2nd ed: The iff-condition for two points to be in the same component of $\mathbb{R}^\omega$
general-topology
proof-verification
connectedness
alternative-proof
path-connected
Proving a sequence is bounded under given conditions
sequences-and-series
proof-verification
derivatives
continuity
alternative-proof
Is there a way to avoid uniform convergence in Urysohn's extension theorem?
general-topology
continuity
soft-question
alternative-proof
Characteristic Polynomial of Restriction to Invariant Subspace Divides Characteristic Polynomial
linear-algebra
matrices
determinant
alternative-proof
minimal-polynomials
Inscribing Platonic solids in each other: why can't you put a dodecahedron in an octahedron?
geometry
alternative-proof
convex-geometry
polyhedra
platonic-solids
Does the functional equation $p(x^2)=p(x)p(x+1)$ have a combinatorial interpretation?
combinatorics
polynomials
generating-functions
alternative-proof
combinatorial-proofs
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
trigonometry
inequality
alternative-proof
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