5.2 The Pigeonhole Principle pg.354

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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?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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