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sufficiently

sufficiently, adv. (n.) (səˈfɪʃəntlɪ) [f. sufficient a. + -ly2.] In a sufficient manner. 1. In a manner or to an extent calculated to satisfy the circumstances of the case or adequate to a certain purpose or object; enough for the purpose (expressed or implied). Formerly also in phr. † sufficiently ... Oxford English Dictionary

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Sufficiently Breathless

Sufficiently Breathless, the second album by Captain Beyond, was released in 1973 and features a jazzier, smoother sound than its predecessor, reminiscent The medley format of the first album is retained only for the last six minutes of Sufficiently Breathless: "Voyages of Past Travellers" flows directly wikipedia.org

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sufficiently

sufficientlyadv: not sufficiently careful 不够细心. 牛津英汉双解词典

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Fed policy rate appears 'sufficiently restrictive': Bowman | Reuters

Jan 8, 2024Reuters, the news and media division of Thomson Reuters, is the world's largest multimedia news provider, reaching billions of people worldwide every day. Reuters provides business, financial ...

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inequality - How to prove $a^n < n!$ for all $n$ sufficiently large ...

Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange

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What is the difference between "arbitrarily close" and "sufficiently close" in term of limits? The definition of limit as always > “the limit of $f(x)$, as $x$ approaches $a$, equals $L$” means we can make the value...

$, equals $L$” means we can make the values of $f(x)$ **arbitrarily close** to $L$ Rephrasing: " _as close as we want_ " > by restricting x to be **sufficiently

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"Sufficiently close" Ring Extensions This problem is from Serre's Local Fields book. I am having difficulty trying to understand what he means by "sufficiently near $x$". Suppose that $B$ (hence also $A$) is a discre...

So, $y$ is sufficiently close to $x$ is $\nu(x-y)$ is large enough.

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Is every sufficiently large even integer the sum of distinct primes? > Is every sufficiently large even integer the sum of (any number of) _distinct_ primes? No doubt this question has been asked before; does the con...

Vinogradov's theorem implies that every sufficiently big odd number is the sum of three primes (since it gives a lower-bound for $r_3(n)$), hence every sufficiently big even number is the sum of four distinct primes.

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Sufficiently rich signals I know that a signal is sufficiently rich of order $n$ when it "includes" at least $\dfrac{n}{2}$ different frequencies. This is intuitive when we are talking about a sine but what about othe...

In your context "sufficiently rich" means "persistent excitation" order.

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Does $w_n = f(n)$ for sufficiently large $n$ $\implies \sum_{i=1}^{j}w_i = \sum_{i=1}^{j}f(i)$ for sufficiently large $j$? Let $w_n$ be a real-valued (EDIT: strictly increasing or decreasing) infinite sequence and let...

Providing a specific example in line with Gae.’s answer, let $f(n)={1\over 10^n}$, and let $w$ be the sequence $47, {1\over100}, {1\over1000}, {1\over10000},\dots$. Then the hypotheses of your question are satisfied. However, $$\sum_{i=1}^{j}w_i = 47.0111\dots{\mbox{ ($j-1$ i’s), but}}$$ $$\sum_{i=1...

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Can I conclude that $ \int_2^x(t\log t)^{-0.9+0.01}dt \le C x^{0.01} $ with sufficiently large $C>0$? Can I conclude that $$ \int_2^x(t\log t)^{-0.9+0.01}dt \le C x^{0.01} $$ with sufficiently large $C>0$?

No. Observe that $\log t\ge\log2$ for $t\ge2$. Then $$ \int_2^x(t\log t)^{-0.89}\,dt\ge(\log2)^{0.89}\int_2^xt^{-0.89}\,dt=\frac{(\log2)^{0.89}}{0.11}\bigl(x^{0.11}-2^{0.11}\bigr). $$

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Show that, for $x$ and $y$ sufficiently tiny, the equation can be solved to $y$ $$e^{\sin{xy}}+x^2-2y-1=0$$ What she meant with "sufficiently tiny"? I think i need go by the theorem about implicit functions, but i rea...

The implicit function theorem says that, under some regularity hypotheses, there is a function $f(x)$ such that the solution set to $F(x,y)=0$ near a particular solution $(x_0,y_0)$ exists and is given by $y=f(x)$. It requires you to have such a point $(x_0,y_0)$ (in your problem they are telling yo...

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exp(X)=A has a solution if A is sufficiently close to identity matrix Can anyone give hint for proving this? I think some kind of inverse thm argument would work. But I wasn't able to make it accurate... such as conti...

Since $\exp(A) = I + A + O(A^2)$, the derivative of $\exp$ at $0$ is the identity map. The inverse function theorem then shows that $\exp$ is invertible in a neighbourhood of $I$.

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Is $n! \nmid n^n$ true for every sufficiently large $n$ (maybe $n \ge 3$)? Is $n! \nmid n^n$ true for every sufficiently large $n$ (maybe $n \ge 3$)? If so, how to prove it? * * * Note that it is easy to show that ...

If $n!|n^ n$ then $n-1$ divides $n^n$. $n$ and $n-1$ are coprime, it follows $n-1$ and $n^n$ are coprime, it follows $n-1$ does not divide $n^n$ unless $n-1=1$ which is not true as $n\geq 3$

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Is there an example of a rational polynomial that has integer output for all integer inputs that are sufficiently large? Is there an example of a rational polynomial $f(n)\in \mathbb{Q}[t]$ that has integer output for...

No. If $f$ has degree $d$, you can reconstruct $f(n-1)$ from $f(n), \ldots, f(n+d)$ by taking repeated differences and adding again.

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sufficiently

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sufficiently

Sufficiently Breathless

sufficiently

Fed policy rate appears 'sufficiently restrictive': Bowman | Reuters

inequality - How to prove $a^n < n!$ for all $n$ sufficiently large ...

What is the difference between "arbitrarily close" and "sufficiently close" in term of limits? The definition of limit as always > “the limit of $f(x)$, as $x$ approaches $a$, equals $L$” means we can make the value...

"Sufficiently close" Ring Extensions This problem is from Serre's Local Fields book. I am having difficulty trying to understand what he means by "sufficiently near $x$". Suppose that $B$ (hence also $A$) is a discre...

Is every sufficiently large even integer the sum of distinct primes? > Is every sufficiently large even integer the sum of (any number of) _distinct_ primes? No doubt this question has been asked before; does the con...

Sufficiently rich signals I know that a signal is sufficiently rich of order $n$ when it "includes" at least $\dfrac{n}{2}$ different frequencies. This is intuitive when we are talking about a sine but what about othe...

Does $w_n = f(n)$ for sufficiently large $n$ $\implies \sum_{i=1}^{j}w_i = \sum_{i=1}^{j}f(i)$ for sufficiently large $j$? Let $w_n$ be a real-valued (EDIT: strictly increasing or decreasing) infinite sequence and let...

Can I conclude that $ \int_2^x(t\log t)^{-0.9+0.01}dt \le C x^{0.01} $ with sufficiently large $C>0$? Can I conclude that $$ \int_2^x(t\log t)^{-0.9+0.01}dt \le C x^{0.01} $$ with sufficiently large $C>0$?

Show that, for $x$ and $y$ sufficiently tiny, the equation can be solved to $y$ $$e^{\sin{xy}}+x^2-2y-1=0$$ What she meant with "sufficiently tiny"? I think i need go by the theorem about implicit functions, but i rea...

exp(X)=A has a solution if A is sufficiently close to identity matrix Can anyone give hint for proving this? I think some kind of inverse thm argument would work. But I wasn't able to make it accurate... such as conti...

Is $n! \nmid n^n$ true for every sufficiently large $n$ (maybe $n \ge 3$)? Is $n! \nmid n^n$ true for every sufficiently large $n$ (maybe $n \ge 3$)? If so, how to prove it? * * * Note that it is easy to show that ...

Is there an example of a rational polynomial that has integer output for all integer inputs that are sufficiently large? Is there an example of a rational polynomial $f(n)\in \mathbb{Q}[t]$ that has integer output for...