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Published: August 5, 2022 (1 week ago)

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FACTORIES AND CHEMICAL PRODUCTION. The industries with the best number of establishments.Q:

How to prove this -surjective function – Abelian Group

In an abelian group $mathbb{G}$, $f:mathbb{Z}^+rightarrowmathbb{Z}^+$ is a bijection such that $a+b=f(a)+f(b)$

How to prove that $f$ is surjective?

I am lost of how to approach this problem because I don’t know if the question is begging for a contradiction or a direct proof.


One way to prove it is to show that for every positive integer $a$, there is a positive integer $b$ such that $f(a)=a+b$.
In fact, if $a$ is odd, let $b=a$. If $a$ is even, let $b=a-2$.
In both cases you can easily verify that $f(a)=a+b$.

IPL GM – Kohli becomes first to score 100 in Twenty20

Kohli became the first batsman to reach 100 as India beat Sri Lanka by seven wickets in a Twenty20 international in Colombo today to go 1-0 up in the four-match series.

T20I @ ACF 2010/11

Sri Lanka 252 for nine in 20 overs (SA Khmar)

Got run out for 28 (SA Khmar)

India 243 for seven in 20.1 overs (MS Dhoni)

Got run out for 20 (AK Bankier)

Got run out for 20 (ZA Khan)

Got run out for 24 (M Sanjeewa)

T20I @ ACF 2010/11

Hari kanth, Run out for 21 (SA Khmar)

IR Butcham, Run out for 19 (M Sanjeewa)

MS Dhoni, Run out for six (N Sathashivamoorthy)

Got run out for one (Sumit Walke)

Got run out for five (A Rahid)

Got run out for 11 (D Bopanna)

Got run out for ten (P de Villiers)

T20I @ ACF 2010/11


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On a souvent plus que ce que vous pourrez la saisir sur le siteMontrose, Vale of Glamorgan

Montrose () is a village in the Vale of Glamorgan, located west of Cardiff, and west of Swansea. Montrose is the name of the parish which it is in. It has a population of 2,830, reducing slightly from the 2001 census.

The village has a primary school, a community centre, a pub/restaurant/coffee shop/butcher’s/ice cream/charity shop/retail store, and a village hall. The local primary school, Asael Academy, was previously the Montrose Primary School, but became an academy in 2007. The history of the Montrose parish is closely linked with that of the slate quarry in the parish. William Buckland, the famous naturalist, was born in Montrose in 1784. Buckland Cliff, a high chalk cliff, is situated on Buckland Hill, two miles from the village. It is a major tourist attraction and is the closest cliffs to Cardiff.

In 2004, the village was named one of the top ten Welsh villages by the BBC.


Before the Romans settled in the area the area was inhabited by the ancient Britons, who called it Heol Penllyn. The Romans built a fort on the top of the Clwydian Fosse called Castell Carnllech in the early 2nd century AD. When the Roman Army moved west, this fort was abandoned, but the name survived in the modern name of the village.

In Roman times, the area was known for its lead-mining and quarrying. The first to exploit the lead mining potential of the area was the Romans. In the year 52 AD the Emperor Claudius invaded South Wales to suppress the Brigantes. In the following five years, his legions devastated and depleted the area around the Vale of Glamorgan.

The History of Tin Mining in Montrose dates back to the early 18