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Titlu: MathOverflow

Descriere: Q&A for professional mathematicians

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Poziţie	Fraza	Pagină	Fragment
1	r frac 1 2	/questions/475302/how-to-define-mathbbr-frac12	How to define $\mathbb{R}^\frac{1}{2} 18 июл. 2024 г. — I want to generate an algebra of dimension 2 − 1 , but there is no CD construction to go from higher to lower dimensions. The question is: ...
3(-2)	ab cd 1	/questions/368901/close-integer-solutions-to-ab-cd-1	Close integer solutions to $ab-cd=1 11 авг. 2020 г. — It is possible with any constant λ> 1 on the place of √2. Take a=t2, d=t2+t− 1 , b=t2+2t+ 1 , c=t2+t+ 1 for large t.
3	n 2 frac 1 n	/questions/461498/proving-sum-i-1n-sum-j-1n-left-fracx-ix-j-right-le-frac	Proving ∑ni=1∑nj=1{xixj}≤914n2？ 3 янв. 2024 г. — OK, here is a fairly simple proof that for any positive integer n and any positive real numbers x 1 ,…,x n , n ∑i,j= 1 {xixj}≤914 n2 .
3	mathrm m 0	/questions/432291/homotopy-type-theory-why-are-0-mathbb-n-and-mathrmsucc0-mathbb-n-not	Homotopy type theory: why are $0:\mathbb N$ and $\ ... 12 окт. 2022 г. — Daniel's answer is correct that the judgmental distinctness of 0 and succ( m ) is not what justifies a definition by pattern-matching.
3	c frac 1 4	/questions/77500/why-the-quarter-in-the-frac14-pinched-sphere-theorem	Why the quarter in the $\frac{1}{4}$-pinched sphere theorem? 8 окт. 2011 г. — Certainly 1/4 is optimal , as Will Jagy points out, for e.g. the Fubini-Study metric on CPn. The totally real tangent planes have curvature 1 ( ...
3	mathrm so 4	/questions/239832/closed-subgroups-of-mathrmso4	Closed subgroups of SO(4) 26 мая 2016 г. — Closed subgroups of SO(4) · It so happens that SO ( 4 ) is almost SO(3) x SO(3) - close enough that one can use the SO(3) result to deal with SO ( 4 ).
3	mathrm f 2	/questions/464109/is-every-automorphism-of-mathrmautf-2-induced-by-conjugation-inside-m	Is every automorphism of $\mathrm{Aut}^+(F_2)$ induced ... 13 февр. 2024 г. — Dyer–Formanek–Grossman showed that Aut+(F2) is isomorph ic to B4/Z4, the quotient of the 4-strand braid group by its centre. (Bridson–Wade give a ...
4(+2)	x 3 y 3 3 n	/questions/58188/are-nontrivial-integer-solutions-known-for-x3y3z3-3	Are nontrivial integer solutions known for $x^3+y^3+z^3=3$? 11 мар. 2011 г. — Infinite families of solutions are known for n =±1, including one constructed by Ramanujan from generating functions (see Rowland's survey).
4(+14)	mathrm h 1	/questions/418528/weak-convergence-in-h1-mathrmloc	Weak convergence in $H^1_{\mathrm{loc}} 20 мар. 2022 г. — The sequence (uk) need not converge in H1 (Ω) under the given hypotheses. Indeed, recall that a weakly convergent sequence is bounded.
4	a 3 frac 1 12	/questions/84663/does-the-equation-1-2-3-dots-frac112-have-a-natural-p-adic-in	frac{1}{12}$ have a natural $p$-adic interpretation? 1 янв. 2012 г. — Does the equation 1 +2+ 3 +⋯=− 112 have a natural p-adic interpretation? · Brian Conrad suggested to me that I study the theory of p-adic zeta ...

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Poziţie	Fraza	Pagină	Fragment
1	r frac 1 2	/questions/475302/how-to-define-mathbbr-frac12	ra.rings and algebras - How to define $\mathbb{ R }^\ frac { 1 }{ 2 }$? So as $ 2 ^{- 1 }$ dimensional space, I pick the set of real numbers, which when written in base $b$, have all zeros in odd-placed digits (counting the lowest significant entire digit as $0$ place). This set of numbers creates a fractal, which, when scale
3	4 left frac 5 11 right	/questions/109288/does-c-left-frac511-right-imply-exponential-growth	gr.group theory - Does $C'\ left (\ frac { 5 }{ 11 }\ right )$ imply... I was therefore wondering if $\ frac { 5 }{ 11 }$ is maybe enough to still have exponential growth. ... Note that $1/5 < 5 / 11 $. See the book by Olshanskii's book "Geometry of defining relations of groups".
6	mathrm q	/questions/2791/understanding-mathrmgal-bar-mathbbq-mathbbq	nt.number theory - "Understanding" $\ mathrm {Gal}(\bar...) I have heard people say that a major goal of number theory is to understand the absolute Galois group of the rational numbers $G = \ mathrm {Gal}(\bar{\mathbb{ Q }...
6	8 mathrm mathrm	/questions/2791/understanding-mathrmgal-bar-mathbbq-mathbbq	nt.number theory - "Understanding" $\ mathrm {Gal}(\bar...) I have heard people say that a major goal of number theory is to understand the absolute Galois group of the rational numbers $G = \ mathrm {Gal}(\bar{\mathbb{Q}...
7	mathrm o	/questions/314766/what-is-mathrmo-q-mathrmso-q-if-q-is-a-quadratic-mathbbz-form-whi	ag.algebraic geometry - What is $\ mathrm { O }_q/\ mathrm ... What is $\ mathrm { O }_q/\ mathrm {SO}_q$ if $q$ is a quadratic $\mathbb{Z}$-form which is degenerate? Ask Question.

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