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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?