Is there an easy way to prove

  • Thread starter tronter
  • Start date
  • #1
186
1
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?
 

Answers and Replies

  • #2
cristo
Staff Emeritus
Science Advisor
8,107
73


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?

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
186
1


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

Or do a contradiction (e.g. assume that it is neither irrational nor rational)?
 
  • #4


that a rational number + an irrational number is either rational or irrational?
Any real number is either rational or irrational, so what's the point of the statement you are trying to prove?
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
41,833
964


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.
 

Related Threads on Is there an easy way to prove

Replies
1
Views
1K
Replies
6
Views
1K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
2K
Replies
1
Views
1K
Replies
4
Views
1K
Replies
21
Views
2K
Replies
5
Views
649
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
7
Views
2K
Top