Thread: irrational numbers

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

Originally Posted by okami

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

If were a rational number then there exist integers and such that:



but then:



but that means is also rational.

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

CB