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Axioms for the Real numbers The algebraic axioms a+b=b+a a·b=b·a (a+b)+c=a+(b+c) (a·b)·c=a·(b·c) a+0=a a·1=a ∀ a ∃ (−a) : a + (−a) = 0 ∀ a ≠ 0 ∃ aˉ¹ : a · aˉ¹ = 1 We can rewrite algebraic axioms as one mathematics statement: a · (b + c) = a · b + a · c The order axioms a > b , b > c ⇒ a > c a > b ⇒ ∀ c, a + c > b + c a > 0, b > 0 ⇒ a · b > 0

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Here are the dictation websites. Tolearnenglish Talkenglish LEARN AMERICAN ENGLISH ONLINE Englishclub Breaking News English Learn English online Listen and Write Listen A Minute.com MyProfe Listen to audio books on our website Audio books Podcast websites. Englishld Spotlight Luke’s ENGLISH Podcast British engVid lessons American British Council BBC. English at work All Ears English Podcast All Ears English Podcast Episode Archive Easy Stories in English English Listening Lesson Library Online

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Day 6 1.I took the flashcard quiz [url=https://easy-english-study.com/voa/]Flashcards VOA Words 61-75[/url]. 2.I read posts from Dual-language Book in English and literal translation into my native language. 3.I took the grammar test Present Perfect or Present Simple and got a mark 100.

Here is the link to sound flash cards [url=https://easy-english-study.com/voa/]Flash cards[/url] Try to do 15 flash cards per day, you can enter a memorizing word in the field or replay it in your memory, do what is more convenient to you, you have to choose an answer Again, Hard, Not hard, Easy. Mention exercises in your diary here. See you in the next lesson. Cheers!

1)It's a rain season now. 2)The weather is bad today. 3)I have to wear a raincoat in autumn. 4)My raincoat is long. 5)Therefore, I don't wear a raincoat when I ride a motorbike. 6)I'm short sighted. 7)I cannot see people clear. 8)Rainwater enters into my eyes very often. 9)My eyes sting because of it. 10)Thus it's very difficult to drive in a rain season for me. 11)After a 10-minute trip I arrive at work.

31st. Rations about half a pound of bread and about four ounces of beef today. 口粮约半磅的面包和大约四盎司的牛肉今天。 These are the best rations we have received for over a week. 这是我们一周来收到的最好的口粮 Men are very anxious to be exchanged so that we can get into our lines once more. 男人们非常渴望被交换，以便我们可以再次进入我们的队伍。

14th. Marched from Jefferson through Sulphur Springs to Culpepper, distance about twenty miles ; got some biscuit and raw bacon, which men ate with great relish. 14. Marschierte von Jefferson durch Sulphur Springs nach Culpepper, Entfernung etwa zwanzig Meilen; bekam etwas Gebäck und rohen Speck, den die Männer mit großem Genuss aßen. Took the cars for Gordonsville and remained there all night; the men are tired; Nahmen die Autos nach Gordonsville und blieben die ganze Nacht dort; die Männer sind müde; the guards strict and will not allow us to purchase anything; prisoners are searched and everything taken from us ; some of the boys hide money in their shoes and stockings to prevent the rebels getting it. die Wachen sind streng und erlauben uns nicht, etwas zu kaufen; Gefangene werden durchsucht und uns alles weggenommen; einige der Jungen verstecken Geld in ihren Schuhen und Strümpfen, um zu verhindern, dass die Rebellen es bekommen.

31st. Rations about half a pound of bread and about four ounces of beef today. 31. Razioni di circa mezzo chilo di pane e circa quattro once di manzo oggi. These are the best rations we have received for over a week. Queste sono le migliori razioni che abbiamo ricevuto durante la settimana. Men are very anxious to be exchanged so that we can get into our lines once more. Gli uomini sono molto ansiosi di essere scambiati in modo da poter entrare di nuovo nelle nostre linee.

18th. One-half of the prisoners will die from sore arms. 18. Metade dos prisioneiros estão morrendo de dor nos braços. They say that it is the same in the rest of the Richmond prisons. Eles dizem que é o mesmo no resto das prisões de Richmond. Some of the best men in the world are almost falling to pieces through the treachery and malice of the doctor against the Northern soldier. Alguns dos melhores homens do mundo estão quase caindo aos pedaços por causa da traição e da malícia do médico contra o soldado do Norte. Brady of my company died today from the effects of the vaccine, his arm almost falling off. Brady, da minha companhia, morreu hoje com os efeitos da vacina, com o braço quase caindo. Poor fellow, how he suffered. Pobre sujeito, como ele sofreu. This is getting to be a horribly sickening place, with suffering of all kinds, disease and starvation. Este está se tornando um lugar repugnante, com sofrimentos de todos os tipos, doenças e fome.

Day and date of greatest number of prisoners at Andersonville — 33,114— August 8th, 1864. Día y fecha del mayor número de prisioneros en Andersonville - 33,114— 8 de Agosto de 1864. Number of Prisoners received during its occupation, 45,613. Número de presos recibidos durante su ocupación, 45.613. Daily average of deaths during its occupation, 29. Promedio diario de muertes durante su ocupación, 29 Ratio of mortality per 1,000 of mean strength, 24 per cent. Relación de mortalidad por 1.000 de fuerza media, 24 por ciento Mortality of 18,000 registered patients, 75 per cent. Mortalidad de 18.000 pacientes registrados, 75 por ciento.

29th, Bread today. Día 29. Hoy hay Pan. They say they must get meal to one half and bread to the other half on alternate days. Dicen que tienen que dar harina a una mitad y pan a la otra mitad en días alternados. Raiders are getting worse every day. Los Asaltantes se ponen peor cada día. Some prisoners escaped from the guards yesterday while out after fire-wood; Captain Wirz started the blood hounds after them. Algunos prisioneros escaparon de los guardias ayer mientras estaban fuera consiguiendo leña; El Capitán Wirz mando a los sabuesos tras ellos.

Trial of Henry Wirz, In the foregoing pages' you will find the name of Capt. Henry Wirz mentioned in several instances as being cruel and inhuman to the Union prisoners. He was tried and convicted of murder, the trial commencing August 23, 1865 and ending October 26, 1865, hundreds of witnesses testified that he committed murder on eleven soldiers who were confined in Andersonville, Ga., prison. He was sentenced to death and the sentence was executed at Washington, D. C. between the hours of 10 and 11 o'clock, Friday morning, November 10, 1865. His body was interred in the Arsenal grounds. (The above was taken from the official report of the trial of Henry Wirz ) (THE END.)