# Is there an easy way to prove

1. Oct 17, 2008

### tronter

Is there an easy way to prove....

that a rational number + an irrational number is either rational or irrational?

Just pick 2 elements and show that it the sum is rational and irrational?

2. Oct 17, 2008

### cristo

Staff Emeritus
Re: Is there an easy way to prove....

That's not a proof, as I explained to you before. A proof must hold true for ALL values, not just one or two.

You need to show some work in the HW forum. What have you tried?

3. Oct 17, 2008

### tronter

Re: Is there an easy way to prove....

Let $$x = \frac{p}{q}$$ and $$y$$ be an irrational number. Then show that this sum leads to a form $$p/q$$ or that it cannot be expressed in that form?

Or do a contradiction (e.g. assume that it is neither irrational nor rational)?

4. Oct 17, 2008

### Pere Callahan

Re: Is there an easy way to prove....

Any real number is either rational or irrational, so what's the point of the statement you are trying to prove?

5. Oct 17, 2008

### HallsofIvy

Staff Emeritus
Re: Is there an easy way to prove....

I think the OP meant prove that the sum of an irrational and rational number must be irrational but wasn't sure whether the result should be "is irrational" or "is rational".

Of course, if m is rational and x is irrational, then x+ m= n with n rational leads immediately to x= m-n, a contradiction.