Simplify the expression 3 1/3/3 1/3. Explain how the expression and its simplified form show that the set of irrational numbers is not closed under division
The expression given is ambiguous according to the standard rules of math (PEMDAS) due to the lack of appropriate parentheses and probably the exponentiation symbol ^.
From the context, I assume it to mean (3^(1/3)) / (3^(1/3)) = 1
Since 3^(1/3) is the cube-root of 3, and is thus irrational. However, the quotient is exactly 1, which is a rational number.
The example is therefore a counter-example for the statement that "set of irrational numbers is closed under division", or stated differently, "the set of irrational numbers is not closed under division"
