Checking if Rationals are Closed Under Addition and Scalar Multiplication

[robierob12]

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?

 

[EnumaElish]

Integers are rationals: 2 = 2/1 = 4/2 = ...

 

[robierob12]

it's always the obvious. how funny