Using the mathod of mathematical induction

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Homework Statement


Let H be a ten- element set of potive integers ranged from 1 to 99. Prove that H has two disjoint subsets A and B so that the sum of the elements of A is equal to the sum of the elements of B.
 
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This is a pigeonhole question, not an induction question.
hint:

If you have 10 different numbers, how many different ways can you choose a subset of them? (to make a sum)and also,

what is the range of answers you can possibly get? (numbers chosen from 1-99 and up to a maximum of 10 numbers)
 

Thread 'Finding the nth roots of a complex number'

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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