• 龙津小学-陆欢仪-语文-端午粽

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    实数的起源

        我们已经学过实数的定义：有理数和无理数统称为实数。呵呵，事实上，可完全没有这么简单。事实上，从人类第一次发现无理数的存在到真正弄清楚什么是实数，中间过去了2000多年，那已经是19世纪末了，数学家意识到必须为微积分奠定一个坚实的逻辑起点了。这个逻辑上的起点就是关于实数的一些基本定理，这些定理第一次准确界定了实数的内涵。
        在那之前很久，数学家们已经通晓了极限的运算，极限运算是微积分的基础，但是从来没有人去说明过极限运算是可行的，或者说在怎样一个范围内极限运算是可行的。举一个例子，在整数范围内乘法运算总是可以的，因为运算结果一定是整数，但除法运算就不可以了，如果你要讨论除法运算，你就必须在整个有理数的范围内进行。但在有理数的范围内，开方运算也是不行的，要进行开方运算，你必须在代数数的范围内。
        那么，数学家和其它科学家已经广泛使用微积分的时候，自然有人会问，我们是在那个数集上进行极限运算的呢？会不会发生什么混乱呢？当然，人们愿意仍然把这个数集称为实数集，但现在的问题是，实数集里面应该有些什么，使得极限运算可以安全的进行？一般来说，人们会假定由所有小数组成的数集就是实数集。但会不会有用这些小数也表示不了的实数呢？
        最后，柯西第一次解决了这个问题，用完备性公理作出了实数集和的明确的定义。他的做法是，作出所有的有理数的数列，然后把所有收敛的数列按极限相同的等价关系进行分类，最后把这些所有的类的集合定义为实数集（有理数集同构于它的一个子集，因此它确实是有理数集的一个扩充）。柯西论证了这个集合上进行极限运算是可以的，这就是实数集的完备性。
        后来，戴德金用分割给出了实数完备性的另一个等价定义，并且证明了无限小数（把有限小数做成后面是9的循环小数）的集合满足完备性公理，因此说明了无限小数的集合就是实数集合。 至此，科学家们才松了一口气，继续放心的使用微积分。

    • listening1

    Listen to the recorder and fill in the blanks with right words.

    1.I have a good famliy that my          love each other very much .

    2. I phone my         every week .

    3.  “How many people are there in your famliy?”

    “          ,                                   ”

    4. We can see 5          on the          .

    5. Where are you going this summer holiday?
    I am going to                                .”

    • Dialogue2

    Searching for Life on Mars

    A robot vehicle which will search for life on Mars will be launched in 2011, it was announced in April 2005. This will be known as the Aurora Mission. European scientists have been frustrated by the failure of Beagle-2 in 2003, but excited by finds of methane (a gas which can be produced by living organisms) by NASA's Spirit and Opportunity rover vehicles in 2004.

    The same European Space Agency exploration programme hopes to bring home pieces of rock from Mars by 2016, and envisages sending men to Mars by the 2030s. The mission to bring rocks and people back from Mars will require nuclear-powered spacecraft to generate enough energy for the return flight. It will also require the help of NASA in the USA.

     
    • Exam2

    m10-u2 test.doc

    • Reading1

      

             Kunming is the capital of Yunnan. It's a city with a long history. Though the weather in Yunnan changes from place to place, Kunming is famous for its beautiful weather. It's neither too hot in summer nor too cold in winter. That's why more and more people like to travel here and even to live here.

                 At weekends or when they are on holiday, people like to relax in different places and in different ways. In winter, people, especially old people, like to climb the Western Hills. From the top of the Hills, you can have a good view of the beautiful scenery of Kunming. Far away from the Hills you can enjoy the Sleeping Beauty among the Hills. After supper, families take a walk along the bank of Dianchi Lake. The Golden Temple and the EXPO Garden are two famous places of interest in the north of the city. The EXPO Garden is known to people both at home and abroad. You can spend a whole day visiting the world-famous garden. A little farther away from the southeast of the city, a special forest welcomes you. It is not a tree forest, but a stone forest. So it is called the Stone Forest.

               People in Kunming are really friendly. They often invite their friends home to try delicious food, like rice noodles. If you want to know more about Kunming and taste the food, why don't you go there yourself!

    • Exam3

    m10-u3 test.doc

    • Dialogue3

    Chinese astronaut to spacewalk on Sep. 27

    An astronaut will spacewalk outside the capsule on the afternoon of September 27, Gu Yidong, the commander-in-chief and chief designer of the spacecraft application system of China’s manned space program, explained to the media on September 23.

    Earlier on September 23, several news portal websites reported that a Shenzhou VII astronaut would spacewalk at 16:30 – the day after launch. They said if Shenzhou VII 
    was launched at 21:10 on September 25, the astronaut would leave the capsule at 16:30 on September 26. However, Gu corrected the reports, explaining that the spacewalk would begin on the day after orbit is achieved. If the launch was on September 25, the spacecraft would enter orbit on 26, and the astronaut would spacewalk on the afternoon of 27.

    Experts said the spacecraft would climb to an altitude of 300 km and then into outer space. Though the astronaut would be protected by the special seat and garment, hewould need a certain period of time to adjust to the environment. He might experience nausea, vomiting or other discomfort if he left the capsule too early.
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