Proving the Impossibility of Non-Intersecting Visitors in a Mathematics Library

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In summary, the question presents a scenario where a mathematics library has several visitors and it is impossible to find three visitors who did not meet in the library that afternoon. The task is to prove that there are two moments in the afternoon where each visitor was present in the library at one of those moments. The question is open to interpretation as it does not specify the exact number of visitors or their movement patterns. Possible approaches include arranging the visitors in a sequence and dividing them into groups based on their overlap with the latest and earliest arrivals. A concern was raised about the lack of information provided in the question.
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rbzima
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Homework Statement



One afternoon, a mathematics library had several visitors. A librarian noticed that it was impossible to find three visitors so that no two of them met in the library that afternoon. Prove that then it was possible to find two moments of time that afternoon so that each visitor was in the library at one of those two moments.

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The Attempt at a Solution



My beef with this question is that it seemingly does not produce enough information. What does several infer?

Here is what I am thinking... Arrange each visitor from [tex]x_{1}[/tex] to [tex]x_{n}[/tex], but after this I have no idea what to do...
 
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Several means 3 or more, here.

It isn't true if a person may enter and leave the library more than once in the afternoon.

If you assume that each person enters and leaves the library only once ... say person A is the one who arrives latest, and B is the one who leaves earliest. If A and B overlap, then they're all there between when A arrives and B leaves.

If A and B don't overlap, then divide the people into two groups, depending on whether they overlap with A or with B ... and take it from there.

Laura
 

1. What is a proof in science?

A proof in science is a logical and empirical demonstration that supports a hypothesis or theory. It involves using evidence and data to support a claim or argument.

2. How is a proof different from a theory?

A proof is a specific piece of evidence or demonstration that supports a theory, while a theory is a broad explanation or framework that explains a range of phenomena. A proof provides evidence for a theory, but a theory can still be considered valid even without a specific proof.

3. Who can provide a proof in science?

Anyone can provide a proof in science as long as they follow the scientific method and provide evidence to support their claims. This can include scientists, researchers, and even students conducting experiments in a classroom setting.

4. How do scientists use proofs in their research?

Scientists use proofs in their research to support their hypotheses or theories. They conduct experiments or gather data to provide evidence for their claims, and then present their findings as a proof to support their argument.

5. Can a proof ever be considered absolute or infallible?

No, a proof in science can never be considered absolute or infallible. This is because new evidence or data can always arise that may challenge or change a previously accepted proof. Science is a constantly evolving field, and what may be considered a proof today may be disproven in the future.

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