What is the Sum of Two Irrational Numbers?

[CollectiveRocker]

I have a question. I realize that two rational numbers added together equal a rational number and that a rational added to a irrational equal a irrational number; but how do I show what a irrational plus a irrational equal?

 

[StatusX]

They can be either. For example, Sqrt(2) + (2 - Sqrt(2)) is rational but Sqrt(2) + Sqrt(3) is not.

 

[CollectiveRocker]

Do I just do two separate cases then?

 

[StatusX]

For what? There's nothing to prove.

 

[CollectiveRocker]

So is it ok for me to just say that then? With no steps of the proof?

 

[dextercioby]

You can say:"When adding two irrational numbers,there's no rule/theorem to tell us the algebric nature of the resulting number"...

Daniel.

 

[Hurkyl]

First, you need to figure out what you're trying to say. Then, worry about how to justify it.