# to show there are irrational numbers

• Mar 14th 2010, 06:25 AM
yanyannn
to show there are irrational numbers
hi everyone.
if we have to prove there are irrational number x and y are the element of Real numbers,
for example 2x-y is rational (by contradiction).
so how would that be? just getting two random numbers and substitute them into the equation? cant work out what it is so please, can anyone help me? thankyou so much!(Bow)
• Mar 14th 2010, 08:45 AM
Hello yanyannn

Welcome to Math Help Forum!
Quote:

Originally Posted by yanyannn
hi everyone.
if we have to prove there are irrational number x and y are the element of Real numbers,
for example 2x-y is rational (by contradiction).
so how would that be? just getting two random numbers and substitute them into the equation? cant work out what it is so please, can anyone help me? thankyou so much!(Bow)

I'm sorry, but you must write in intelligible English if we are to understand what you mean. This just doesn't make sense.

Please set out what you mean as carefully and as precisely as you can.

I might be wrong but, substituting random number as x;y doesnt give you anything. You have to substitute an irrational number and then prove that it can not be written as rational. (that is in the form of $\displaystyle \frac{a}{b}$)
A classical example is $\displaystyle \sqrt{2}$ There is a irrational number, and the proof very old, checking that proof could give you an idéa, (it is done by contradiction).