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1m
comment how to show $\mathbf{Q} $ is not free
@annimal $1/4+1/4=1/2$. If $r_1,\ldots,r_n$ is a finite set of generatos, let $p_1,\ldots,p_r$ be the set of all primes in the denominators. Then $x=1/(p_1\ldots p_r)$ is a generator.
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revised how to show $\mathbf{Q} $ is not free
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revised how to show $\mathbf{Q} $ is not free
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comment What are some remarkable and interesting uses of AM-GM Inequality ? Cite and explain with problems.
You can use that $t\leqslant \exp({t-1})$.
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comment how to show $\mathbf{Q} $ is not free
@MarianoSuárez-Alvarez I was addressing "But how to show Q is not finitely generated?". I will address freedom in a minute. =)
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answered how to show $\mathbf{Q} $ is not free
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comment Is $(G,*)$ commutative?
@AAA You're misinterpreting the OPs question. The question is "Suppose that for some integers $i,i+1,i+2$ we have $a^jb^j=(ab)^j$ for any $a,b\in G$. Then $G$ is commutative."
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comment Is $(G,*)$ commutative?
This is not correct. Take a non abelian group of even order, for example $S_3$.
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comment Prove that $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic as groups
Note that $\Bbb Q$ is an abelian group that is divisible, but $\Bbb Z$ is not.
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comment Determinant: Alternative Definition (Matrices)
@Mathemagician1234 I have tried to simplify this idea in my answer.
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revised Determinant: Alternative Definition (Matrices)
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answered Determinant: Alternative Definition (Matrices)
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comment Is $(G,*)$ commutative?
@BrunoJoyal He means that for three integers $i=j,j+1,j+2$, one has $(ab)^i=a^ib^i$. The answer is positive.
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revised Interchanging the order of a double infinite sum
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answered Interchanging the order of a double infinite sum
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revised Continuity of Modified Hom Functor
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comment Why $1$ isn't a prime?
@Batman The correct answer in the general contexts of UFDs is that primes are non units, and 1 is a unit in the ring of integers.
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comment Every invertible linear transformation can be perturbed a bit without destroying invertbility, Neumann series
$1-\varepsilon T$ is invertible iff $\varepsilon$ is not an eigenvalue of $T$. If $V$ is finite dimensional, $T$ has finitely many eigenvalues.
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awarded  Nice Answer
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comment How to prove $\lim\limits_{t \to 1^-} \frac{\sqrt{1-t^2}}{2\pi}\int_{S^1}\frac{f(x,y)}{1-tx}ds=f(1,0)$?
Your title was uninformative and subjective. I've changed it to a more informative and objective one. Please consider this for future posts.