What is the Sum of Two Irrational Numbers?

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    Irrational Proof
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Homework Help Overview

The discussion revolves around the properties of irrational numbers, specifically focusing on the sum of two irrational numbers and whether it can be classified as rational or irrational. Participants explore the implications of adding irrational numbers and the lack of definitive rules governing the outcome.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss examples of sums of irrational numbers, questioning whether the result can be rational or irrational. There is a consideration of how to approach the proof or justification of these properties.

Discussion Status

The conversation is ongoing, with participants exploring different perspectives on the nature of sums involving irrational numbers. Some guidance has been offered regarding the absence of a definitive rule for the outcome of such sums, and there is an emphasis on clarifying the underlying concepts before attempting to justify them.

Contextual Notes

Participants are navigating the complexities of irrational numbers and their sums without a clear framework for proof, indicating a potential gap in foundational understanding or assumptions about the properties of these numbers.

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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