Checking if Rationals are Closed Under Addition and Scalar Multiplication

robierob12
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Homework Statement



Check to see if the (vector space) set of rational numbers is closed under addition and scalar multiplication

Homework Equations



The book says this holds for addition but fails for scalar multiplication.

The Attempt at a Solution



Im a little confused. You can add two of the same rational number like (1/2) and (1/2) and get an integer. Now your out of the vector space. Where is my logic failing me?
 
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Integers are rationals: 2 = 2/1 = 4/2 = ...
 
it's always the obvious. how funny
 

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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