Are the Results of These Irrational Number Operations Also Irrational?

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Discussion Overview

The discussion revolves around the nature of operations involving irrational numbers and positive integers, specifically whether the results of such operations remain irrational. Participants explore the implications of multiplying an irrational number by a positive integer and subtracting an irrational number multiplied by any integer from a positive integer.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • Some participants propose that multiplying an irrational number by any positive integer results in an irrational number.
  • Others argue that subtracting an irrational number (multiplied by any integer) from a positive integer also yields an irrational number.
  • A participant suggests a method to prove the irrationality of the results by isolating the irrational number and demonstrating a contradiction.
  • There is a request for clarification on the term "any +ve integer," which is confirmed to mean positive integer.
  • One participant reiterates the conclusion that both operations yield irrational results, referencing the earlier proof method.

Areas of Agreement / Disagreement

While some participants agree on the irrationality of the results, the discussion includes various interpretations and methods of proof, indicating that multiple competing views remain and the discussion is not fully resolved.

Contextual Notes

Limitations include the lack of formal definitions for the terms used and the potential for different interpretations of the operations involving irrational numbers.

Who May Find This Useful

This discussion may be of interest to those studying properties of numbers, particularly in the context of irrationality and mathematical proofs.

spidey
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wat are the answers for these in terms of rational,irrational

(irrational number)*(any +ve integer) = ?
(any +ve integer) - (irrational number)*(any integer) = ?

are the answers also irrational numbers
 
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But of course! Think about it. In both cases, pretend that they give rational numbers. Then isolate the irrational number. See the contradiction?
 
What is "any +ve integer"?
 
mathman said:
What is "any +ve integer"?

positive integer
 
spidey said:
wat are the answers for these in terms of rational,irrational

(irrational number)*(any +ve integer) = ?
(any +ve integer) - (irrational number)*(any integer) = ?

are the answers also irrational numbers

Why not prove it.

In your first example start with

x*n=p/q

Dividing both sides by n gives:
X=p/(q*n) which implies x is rational which is a contradiction.
 
Thanks John...so answer for first one is irrational so second should also be irrational...
 
spidey said:
Thanks John...so answer for first one is irrational so second should also be irrational...

Apply the same method and work it out.
 

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