5.2 The Pigeonhole Principle pg.354

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In summary, the Pigeonhole Principle is a fundamental mathematical concept that states if there are more items than containers, then at least one container must have more than one item. It is used in various mathematical problems and is considered a formal theorem. It can also be applied to real-life situations, such as organizing items or solving problems related to data analysis.
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modzz
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Show that if there are 100,000,000 wage earners in the United States who earn less than 1000,000 dollars, then there are two who earned exactly the same amount of money, to the penny, last year.

There are no equations.


Please solve the question. I really need this question. Thanks
 
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You need to show your ideas, so we can work together and get the solution, so let's start with the basics:

If this is true, why would it be true? How many possible incomes are possible?
 

1. What is the Pigeonhole Principle?

The Pigeonhole Principle is a mathematical concept that states that if there are more pigeons than pigeonholes, then at least one pigeonhole must contain more than one pigeon. In other words, if there are n items and k containers, and n > k, then at least one container must contain more than one item.

2. How is the Pigeonhole Principle used in mathematics?

The Pigeonhole Principle is used in a variety of mathematical problems, including combinatorics, number theory, and graph theory. It is often used to prove the existence of solutions to problems by showing that there must be at least one solution based on the number of objects and containers involved.

3. Can you give an example of the Pigeonhole Principle in action?

One example of the Pigeonhole Principle is the "birthday problem," which asks how many people need to be in a room for there to be a 50% chance that two people share the same birthday. The answer is only 23 people, thanks to the Pigeonhole Principle.

4. Is the Pigeonhole Principle a formal theorem?

Yes, the Pigeonhole Principle is a formal theorem in mathematics. It is often used as a tool to prove other theorems and is considered a fundamental principle in combinatorics.

5. How does the Pigeonhole Principle relate to real-life situations?

The Pigeonhole Principle can be applied to real-life situations, such as organizing items in a limited space or scheduling appointments. It can also be used to solve problems related to data analysis and distribution.

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