What is the Sum of Two Irrational Numbers?

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SUMMARY

The discussion centers on the algebraic nature of the sum of two irrational numbers. It is established that while the sum of two rational numbers is rational, the sum of two irrational numbers can be either rational or irrational, depending on the specific numbers involved. For instance, the sum of Sqrt(2) and (2 - Sqrt(2)) results in a rational number, whereas Sqrt(2) plus Sqrt(3) yields an irrational number. The conversation emphasizes that there is no definitive theorem governing the sum of two irrational numbers, and participants suggest that a proof may not be necessary.

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CollectiveRocker
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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?
 
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They can be either. For example, Sqrt(2) + (2 - Sqrt(2)) is rational but Sqrt(2) + Sqrt(3) is not.
 
Do I just do two separate cases then?
 
For what? There's nothing to prove.
 
So is it ok for me to just say that then? With no steps of the proof?
 
You can say:"When adding two irrational numbers,there's no rule/theorem to tell us the algebric nature of the resulting number"...

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

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