Speech exercises

I. Read and reproduce.

Subsets

Often one set is part of some other set. The set of all women is part of the set of all human beings; the set of all even numbers is part of the set of all whole numbers. Again the phrase “part of” has unfortunate connotations, and mathematicians have been forced to invent a new word to denote the precise concept involved.

A set S is said to be a subset of a set T provided that every member of S is a member of T. Every member of the set W of all women is a woman, hence a human being, hence a member of the set H of all human beings. So W is a subset of H. We use the notation

W H

to describe this, so the symbol should be read as “is a subset of”. We also say that W is contained in H. Certain facts follow at once from our definition of “subset”. Every set is a subset of itself – because all of its members are members of it. Further, the empty set Ø is a subset of any set you care to name. If it were not a subset of a given set S, then there would have to be some element of Ø which was not an element of S. In particular there would have to be an element of Ø. Since Ø has no elements this is impossible.

One nice property of subsets is that a subset of a subset is itself a subset: if A B and B C then A C. For if every element of A is an element of B, and if every element of B is an element of C, then every element of A is an element of C.

II. Topics for discussion:

1. Often one set is part of some other set.

2. Every set is a subset of itself.

3. A subset of a subset is itself a subset.

III. Say this in English.

Множество – это набор, совокупность, собрание каких-либо объектов, называемых его элементами и обладающих общим для всех их характеристическим свойством. “Множество есть многое, мыслимое нами как единое” (Кантор). Это не является в полном смысле логическим определением понятия множества, а всего лишь пояснением (так как определить понятие – значит найти такое родовое понятие, в которое данное понятие входит в качестве вида, но множество – это, пожалуй, самое широкое понятие математики и логики). При этом можно либо дать перечень элементов множества, либо правило, по которому можно определить, принадлежит или нет данный объект рассматриваемому множеству. Это правило часто называют характеристическим свойством множества.

T E X T III

Ordinary differential equations

GRAMMAR: THE GERUND

Forms of the gerund

	INDEFINITE	PERFECT
ACTIVE	writing	having written
PASSIVE	being written	having been written

Exercises:

I. Write a gerund form of the verbs:

1. Active: to note, to represent, to give, to connect, to use, to read, to help, to perform, to classify.

2. Passive: to consider, to find, to produce, to reach, to show, to satisfy, to denote, to discuss, to involve.

II. State the form of the gerund.

1. Taking regular exercise is the most important thing you can do to take care of your health. 2. They spoke about visiting their friend. 3. Why don’t you do the work properly without being reminded? 4. He doesn’t like praising people. 5. She doesn’t like being praised in the presence of her friends. 6. The boy was thanked for having helped this woman when she was in trouble. 7. They finished discussing the report at 2 o’clock. 8. Most of all we were sad about having to leave all of our school friends. 9. Speaking very loud is not allowed here.

III. Translate the following sentences from English into Russian. Pay attention to the functions of the gerund.

1. the gerund is used as a subject.

1. Getting up early is my habit. 2. Talking without thinking means shooting without aim. 3. Reading good books is always useful. 4. Running when you have got a cold is bad for your health. 5. Dancing is actually very good exercise if you do it regularly. 6. Crying over spilt milk is useless. 7. Listening to music is a different matter. 8. Being in a room where I can’t see the exit makes me a bit uncomfortable. 9. Writing poems is my pleasure.

2. The gerund is used as a direct object.

1. He hates wearing a warm coat. 2. She preferred staying at home. 3. I don’t like walking slowly. 4. He enjoys travelling by car. 5. They prefer playing games to watching them. 6. Ann very much enjoys taking photos of animals. 7. I like playing tennis, but I can’t really get excited about running.

c) The gerund is used as a prepositional object.

1. He was surprised at hearing the news. 2. He insisted on doing the work quickly. 3. I think of making her a present. 4. Everyone feels tired of doing one thing for a long time. 5. I’ve been getting more interested in gardening recently. 6. Thomas Edison was well-known for working very long hours. 7. Everything depends on your being here in time.

d) The gerund is used as an attribute.

1. What ways of learning words do you find most effective? 2. I can’t improve my English because I haven’t much chance of speaking it. 3. She found many ways of being useful to him. 4. The idea of painting came to him when he was very young. 5. I can’t understand your way of doing it. 6. The pupils didn’t like the idea of rewriting the text. 7. As time went on, the idea of being a diplomat became less attractive.

e) The gerund is used as an adverbial modifier.

1. On arriving in London we went sightseeing after leaving the luggage in the hotel. 2. I’m going to take a short holiday after finishing this job. 3. Save money by shopping around to find where things are cheaper. 4. I learn a lot by reading. 5. If you want to wake up at a certain time, say the time to yourself three times just before going to sleep. 6. You should wash your hands before eating. 7. The thieves got into the house by breaking a window and climbing in. 8. After doing the same job for ten years, I felt I needed a change.

6. The gerund is used as a part of the predicate.

1. I have just begun understanding how this organization really works. 2. They finished playing tennis an hour ago. 3. When did you stop playing the violin? 4. Will you stop teasing him? 5. Don’t bother locking the door. 6. The minister went on talking for two hours.

IV. State the form and the function of the gerund. Translate the sentences into

Russian.

1. I remember meeting him before the holidays. 2. He was interrupted by someone’s knocking at the door. 3. I am not very interested in discussing your problems. 4. She needs to work without being disturbed. 5. Instead of eating at home, we went to a restaurant. 6. We insisted on carrying out another experiment to check the results. 7. We began by explaining the situation. 8. Can you find a good way of organizing things properly. 9. Our dishwasher keeps flooding. 10. I can’t drive through a tunnel without worrying about what would happen if the roof fell in.

V. Use the gerund in the following sentences.

1. I don’t like (to sing), I prefer (to dance). 2. If you continue (to do) that, you’ll get yourself in trouble. 3. She dislikes (to type) but she has to do it. 4. I am delighted you enjoy (to read) but this is not the time for it. 5. We didn’t want to postpone (to go) there. 6. I couldn’t finish because my pen broke. 7. I am tired of (to listen) to your excuses. 8. The idea of (to travel) by train seems old-fashioned to most teenagers. 9. After (to wait) for half an hour we went home. 10. For (to make) short journeys in city you can use the bus or the underground. 11. Without (to know) her address we could not go to see her.

VI. Change the sentences according to the model:

MODEL: It is interesting to read books. – Reading books is interesting.

1. It is necessary to visit him today. 2. It is important to do this work in time. 3. It is useless to wait for him here. 4. It is more difficult to speak French. 5. It is useful for one’s health (to eat) good quality food. 6. It is quite possible to translate this article without the dictionary. 7. It is impossible to start the car when it is cold. 8. It is pleasant to walk in the park. 9. It is necessary to read through the exam paper carefully. 10. It is easy to check the solution of the problem.

VII. Finish the following sentences using the verbs given in brackets.

MODEL: You can learn to read fluently (to read a lot). - You can learn to read fluently by reading a lot.

1. You can improve your English (to learn grammar, to read a lot, to listen to tapes, to watch films). 2. You will help us (to take part in this work, to give us your advice, to organize the work properly). 3. He can improve his health (to take regular exercise, to do morning exercises regularly, to walk a lot).

VIII. Translate the following word combinations:

1. On hearing about the meeting, on arriving at the station, on entering the room, on learning about the expedition, on hearing the news;

2. The habit of smoking, the way of doing it, the necessity of organizing it, the hope of meeting them, the chance of winning the prize, the way of travelling, the pleasure of seeing you.

IX. Translate into English using the following models:

1. I can’t help laughing. Я не могу не смеяться (не принимать участия в этом состязании, не сказать вам об этом, не любить их, не пригла-сить ее).

2. It’s no use going there. Бесполезно идти туда (пытаться сделать это еще раз, искать эту книгу, объяснять это ему, говорить с ними).

3. We enjoyed hearing this opera. Мы получили удовольствие, слушая эту оперу (читая эту книгу, слушая вашу музыку, участвуя в соревновании, делая эту работу, посещая его выставки).

4. Do you mind … going home now? Вы не возражаете пойти домой? (пойти в кино, пообедать, остаться здесь, встретить его, пойти в столовую).

5. I remember seeing him. Помню, что видел его (давал ей эту книгу, учил эти слова, разговаривал с ним, читал эту книгу, переводил эти статьи).