Infinity - Marvel EDU

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Practice Listening: Highlight Correct Summary ID: #4618 Medium Infinity

Instructions ›

You will hear a recording. Click on the paragraph that best relates to the recording.

Transcript:

For many of us, infinity may be a difficult concept to grasp, but historically there had been no clear definition at all—until the nineteenth century, that is. At that point, mathematicians agreed to define infinity as a set of objects so numerous that it can't be made any larger by adding to or doubling it; nor can it be reduced by subtracting from or halving it. The paradox of infinity was illustrated by a German mathematician in 1924 using the metaphor of a hotel. In a public lecture, he asked the audience to imagine a hotel with an infinite number of rooms. One night the hotel is full, but a traveller arrives who needs a room. The hotel accommodates him by asking the guest in room number I to move to room number 2, and the guest in room number 2 to move to room number 3, and so on. Because the hotel has infinite rooms, this shifting can be infinitely repeated. To take the concept of infinity further, you could imagine that between the numbers I and 2, there are also an infinite number of fractions: a half, a quarter, an eighth, a sixteenth and so on. However, not all numbers can be expressed as fractions; some can only be expressed using decimals (the square root of 2 is a case in point), which means that there is another type of infinity that can only be expressed by imagining an infinite number of points between I and 2, for example, and matching each one to a decimal number.

* Click on the correct answer

Infinity is a difficult concept to grasp. But 200 years ago, a German mathematician was able to relate to an audience how whole numbers and fractions could replace decimal numbers. In the lecture, he used a hotel as an example of how to do this. In the nineteenth century it was discovered that infinity was based on integers and fractions. A German lecturer showed the concept using the metaphor of a hotel, but he was unable to illustrate how decimal infinity was defined. Later, it was described by imagining decimal numbers between whole ones. One mathematical concept is that of infinity, which shows how a full hotel could accommodate more visitors if they are willing to move rooms. Another definition of it uses decimal points that are placed between two numbers like 1 and 2. Mathematicians in the 1800s discovered a way of describing infinity using numbers. It was related by one European who used the analogy of a hotel at maximum capacity making room for an extra guest. But this doesn't take into account that there may be more than one kind of infinity.

Result:

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Option 4: "Mathematicians in the 1800s discovered a way of describing infinity using numbers. It was related by one European who used the analogy of a hotel at maximum capacity making room for an extra guest. But this doesn't take into account that there may be more than one kind of infinity."

Explanation: This option accurately summarizes the main idea of the text, highlighting the historical context of the discovery of infinity in the 1800s and the use of the hotel analogy to illustrate the concept. It also acknowledges the existence of multiple types of infinity, which is a crucial point made in the text. The phrasing is consistent with the text's tone and captures the essence of the discussion on infinity.

Option 1: "Infinity is a difficult concept to grasp. But 200 years ago, a German mathematician was able to relate to an audience how whole numbers and fractions could replace decimal numbers. In the lecture, he used a hotel as an example of how to do this."

Explanation: This option incorrectly states that the mathematician related how whole numbers and fractions could replace decimal numbers. The text emphasizes that there are different types of infinity, including decimal representations, rather than suggesting one replaces the other. Additionally, it misrepresents the timeline by stating '200 years ago' instead of the nineteenth century.

Option 2: "In the nineteenth century it was discovered that infinity was based on integers and fractions. A German lecturer showed the concept using the metaphor of a hotel, but he was unable to illustrate how decimal infinity was defined. Later, it was described by imagining decimal numbers between whole ones."

Explanation: This option inaccurately claims that the lecturer was unable to illustrate how decimal infinity was defined. The text clearly states that there is a type of infinity that can be expressed using decimals, which contradicts this option. Furthermore, it simplifies the concept of infinity to just integers and fractions, missing the broader context presented in the text.

Option 3: "One mathematical concept is that of infinity, which shows how a full hotel could accommodate more visitors if they are willing to move rooms. Another definition of it uses decimal points that are placed between two numbers like 1 and 2."

Explanation: While this option captures the hotel metaphor, it fails to convey the historical context and the significance of the discovery of infinity as a concept. It also oversimplifies the explanation of decimal infinity, neglecting the complexity of the relationship between whole numbers, fractions, and decimals as described in the text.

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