attemptation

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1
attemptation
† attempˈtation Obs. rare—1. [ad. L. attemptātiōn-em, n. of action f. attemptāre to attempt. See also attentation.] An attempting.1425 Paston Lett. 5 I. 21 The attemptacion of diverses matieres a geyn summe frendes of the seyd John. Oxford English Dictionary
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attend, v. meanings, etymology and more - Oxford English Dictionary
The earliest known use of the verb attend is in the Middle English period (1150—1500). OED's earliest evidence for attend is from around 1315, in the writing of Shoreham. attend is a borrowing from French. Etymons: French atendre. See etymology. Nearby entries. attemptation, n. 1425;
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attentation
† attenˈtation Obs. [ad. L. attentātiōn-em, n. of action f. attentāre: see attent v.] = attemptation; ‘a trying or essaying.’ Bullokar 1676.a 1670 Hacket Abp. Williams i. 99 (D.) The Devil that spies the first spark of attentation, and blows it into a flame. Oxford English Dictionary
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attemption
† aˈttemption Obs. rare—1. [irreg. for attemptation.] An attempt.1565 R. Lindsay Hist. Scot. (1728) 33 The English Attemptions were punished in the last Battle. Oxford English Dictionary
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Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime. If $A$ and $B$ are finite subgroups, of orders $m$ and $n$, respectively, of the abelian group $G$, Prove that $AB$ is a subgroup of or...
$AB $ is a subgroup because $G$ is abelian. We know that $$|AB| = \frac{|A| \cdot |B|}{|A \cap B|}$$ But if $\gcd(m,n) = 1$ then $|A \cap B| = 1 $ because $|A \cap B| \mid |A| = m$ and $|A \cap B| \mid |B| = n$ by Lagrange theorem. So $$|AB| = |A| \cdot |B| = mn$$
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a Problem about Special Sequence I am doing homework. And this question may related to #Proving statement about sequences. However, I want to consider the limit of it. Let we assume $a_1=a,b_1=b,b>a>0$. Then we consi...
Yes, $(2)$ is easy once you notice that $a_{n+1}b_{n+1}=a_nb_n$, so the product (and hence also the geometric mean) is invariant. As it is well-know that it is between the harmonic and arithmetic mena, the limit of our nested intervals must equal $\sqrt{ab}$. A similar approach works for $(1)$: Show...
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