# irrational numbers

• Oct 30th 2009, 07:45 AM
okami
irrational numbers
Can anyone help me with this?
"if x is an irrational number, is 2x rational or irrational? explain"

• Oct 30th 2009, 07:52 AM
CaptainBlack
Quote:

Originally Posted by okami
Can anyone help me with this?
"if x is an irrational number, is 2x rational or irrational? explain"

If $2x$ were a rational number then there exist integers $a$ and $b$ such that:

$2x=\frac{a}{b}$

but then:

$x=\frac{a}{2b}$

but that means $x$ is also rational.

So if $x$ is irrational $2x$ must also be irrational as otherwise we have a contradiction (we would have $x$ both rational and irrational and that is not possible).

CB