OpenLLM-France/wikimedia huggingface dataset:
# History of Sri Lanka/Rajendra Chola I

Rajendra Chola I (Rajendra Chola the Great; முதலாம் இராசேந்திர சோழன்) was an emperor of the Chola dynasty in medieval India. He was the son of Rajaraja Chola I. He became the king of the empire in 1014 AD after his father, Rajaraja Chola I died. He had been made co-regent in 1012 AD. He was one of the greatest rulers and military leaders of the Chola Empire, standing with a great army, including navy.

## Ruling over Ceylon

In 1018 AD, Rajendra Chola I continued his father's work and set off a campaign in Illam, Ceylon (present day Sri Lanka) and captured the Sri Lankan capital of Anuradhapura. He later turned to controlling and taking over all of the country/land of Ceylon. As a result of this abrupt invasion on Sri Lanka and the over-taking of Anuradhapura, the former Sinhalese king, Mahinda V, was taken as a prisoner and transported to India. He died, 12 years later, at a prison.
# History of Sri Lanka/S. J. V. Chelvanayakam

Samuel James Veluppillai Chelvanayakam (also spelled Chelvanayagam, 31 March 1898 - 26 April 1977, சாமுவேல் ஜேம்ஸ் வேலுப்பிள்ளை செல்வநாயகம்) was a Ceylonese lawyer and politician. He was a Member of Parliament and was a political leader of the Sri Lankan Tamil community for more than two decades. His son Chandrahasan followed his fathers footstep by becoming a public servant in Tamil Nadu.
# History of Sri Lanka/Ponnambalam Arunachalam

Sir Ponnambalam Arunachchalam (14 September 1853 – 9 January 1924) was a Ceylonese statesman, who served as a member of the Executive Council and the Legislative Council.

## Early life

His father was Gate Mudaliyar Arunachalam Ponnambalam and mother was Sellachchi Ammaiyar. He was the third son of their parents and the younger brother of Sir Ponnambalam Ramanathan who was another famous Ceylon Tamil leader. He was educated at the Colombo Academy (Royal College Colombo), Colombo, and at Christ's College, Cambridge.
He married Swarnambal Namasivayam and had three sons, Sir Arunachalam Mahadeva, KCMG; Sivananthan Arunachalam and Arunachalam Ramanathan.

## Career

He was one of the first Ceylonese to enter the Ceylon Civil Service in 1875. He was appointed General in 1887. He showed his positive work in all the positions he held. On his retirement from the Public Service in 1913, he was honored in recognition of his service to the country. He was also nominated by the Governor to a seat in the Executive Council.
# Polynomial function/R/(X-a)^n divides/Zero of derivative/Exercise

Let $P\in \mathbb {R} [X]$ be a polynomial, $a\in \mathbb {R}$ and $n\in \mathbb {N}$. Prove that $P$ is a multiple of $(X-a)^{n}$ if and only if $a$ is a zero of all the derivatives $P,P^{\prime },P^{\prime \prime },\ldots ,P^{(n-1)}$.
# Polynomial/x^4-x^3/Discussion/Extrema/Exercise

We consider the function
    $F(x)=x^{4}-x^{3}\,.$
* Determine the zeroes of this function.
* Determine on which intervals the function is positive or negative is.
* Determine the extrema of this function.
# Polynomial function/Function behavior from differentiability/Fact

A real polynomial function
    $f\colon \mathbb {R} \longrightarrow \mathbb {R}$
of degree $d\geq 1$ has at most $d-1$ local extrema, and one can partition the real numbers into at most $d$ intervals, on which $f$ is alternatingly strictly increasing or strictly decreasing.
# Polynomial/x^3+x-1/Zero between 0 and 1/Computation/Exercise

Consider
    $f(x)=x^{3}+x-1.$
a) Prove that the function $f$ has in the real interval $[0,1]$ exactly one zero.
b) Compute the first decimal digit in the decimal system of this zero point.
c) Find a rational number $q\in [0,1]$ such that $\vert {f(q)}\vert \leq {\frac {1}{10}}$.
# Polynomial equation/In words/1/Exercise

Does there exist a real number such that its third power, reduced by the fourfold of its second power, equals the square root of $42$?
# Polynomial function/In words/2/Exercise

Does there exist a real number, which, in its fourth power, reduced by the double of its third power, equals the negative of the square root of $42$?
# Polynomial function/Function behavior from differentiability/Fact/Proof/Exercise

Prove that a real polynomial function
    $f\colon \mathbb {R} \longrightarrow \mathbb {R}$
of degree $d\geq 1$ has at most $d-1$ extrema, and moreover the real numbers can be divided into at most $d$ sections, where $f$ is strictly increasing or strictly decreasing.
# Polynomial/f(0) is 1,f(1) is 2,f(2) is0,f(-1) is1/System/Exercise

Find a polynomial
    $f=a+bX+cX^{2}+dX^{3}\,$
with $a,b,c,d\in \mathbb {R}$, such that the following conditions hold.
    $f(0)=1,\,f(1)=2,\,f(2)=0,\,f(-1)=1.$
# Polynomial/f(i) is 1,f(1) is 1+i,f(1-2i) is -i/System of equations/Exercise

Find a polynomial
    $f=a+bX+cX^{2}\,$
with $a,b,c\in \mathbb {C}$, such that the following conditions hold.
    $f({\mathrm {i} })=1,\,f(1)=1+{\mathrm {i} },\,f(1-2{\mathrm {i} })=-{\mathrm {i} }.$
# Polynomial function/Degree d/Maximal number of maxima and minima/Exercise

Let
    $f\colon \mathbb {R} \longrightarrow \mathbb {R}$
be a polynomial function of degree $d\geq 1$. Let $m$ be the number of local maxima of $f$ and $n$ the number of local minima of $f$. Prove that if $d$ is odd then $m=n$ and that if $d$ is even then
    $\vert {m-n}\vert =1\,.$
# Information Organization/Dewey Decimal Classification

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# Information Organization/Collection Analysis

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# Information Organization/Dublin Core

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# Information Organization/Folksonomies

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# Information Organization/Cataloging of Integrating Resources

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# Information Organization/Encoded Archival Description

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# Information Organization/Library of Congress Subject Headings

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# Information Organization/Acquisitions

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# Information Organization/Library of Congress Classification

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# Sequence/Square root of rational function/Exercise

Determine the limit of the sequence
    $x_{n}={\sqrt {\frac {7n^{2}-4}{3n^{2}-5n+2}}},\,n\in \mathbb {N} .$
# Sequence/2n+5\sqrt(n)+7 by -5n+3\sqrt(n)-4/Exercise

Determine the limit of the real sequence given by
    $x_{n}={\frac {2n+5{\sqrt {n}}+7}{-5n+3{\sqrt {n}}-4}}\,.$
# Sequence/Cauchy sequence in Q/Not convergent/Exercise

Give an example of a Cauchy sequence in $\mathbb {Q}$, such that (in $\mathbb {Q}$) it does not converge.
# Sequence/Recursive/Square root of xn+1/Limit/Exercise

The sequence ${\left(x_{n}\right)}_{n\in \mathbb {N} }$ is recursively defined by $x_{0}=1$ and
    $x_{n+1}={\sqrt {x_{n}+1}}\,.$
Show that this sequence converges and determine its limit.
# Sequence/Square root of n/Divergence/Exercise

Prove that the sequence ${\left({\sqrt {n}}\right)}_{n\in \mathbb {N} }$ diverges to $\infty$.
# Sequence/Partial sum of unit fractions/Exercise

Show that the sequence $(a_{n})_{n\in \mathbb {N} }$ with $a_{n}={\frac {1}{n+1}}+\cdots +{\frac {1}{2n}}$ converges.
# Sequence/3n^3-5n^2+7 over 4n^3+2n-1/Under 2x^4-6x^3+x^2-5x+3/Exercise

Compute the limit of the sequence
    $b_{n}=2a_{n}^{4}-6a_{n}^{3}+a_{n}^{2}-5a_{n}+3\,,$
where
    $a_{n}={\frac {3n^{3}-5n^{2}+7}{4n^{3}+2n-1}}\,.$
# Sequence/Rational and trigonometric/2/Exercise

Decide whether the sequence defined by
    $x_{n}:={\frac {5\sin ^{3}n-6n^{4}+13n^{2}+{\left(\sin n\right)}{\left(\cos {\left(n^{2}\right)}\right)}}{7n^{4}-5n^{3}+n^{2}\sin ^{2}{\left(n^{3}\right)}-\cos n}}\,$
converges in $\mathbb {R}$ and determine, if applicable, the limit.
# Sequence/Square root of n power n by n!/Exercise

Examine the convergence of the following real sequence $x_{n}={\frac {{\sqrt {n}}^{n}}{n!}}$.
# Sequence/2n+1 over n/Under 5x^3-4x^2+2x-3/Exercise

Compute the limit of the sequence
    $x_{n}=5\left({\frac {2n+1}{n}}\right)^{3}-4\left({\frac {2n+1}{n}}\right)^{2}+2\left({\frac {2n+1}{n}}\right)-3\,$
for $n\rightarrow \infty$.