Irrational + irrational = rational

In summary, the conversation discusses the existence of two irrational numbers, x and y, whose sum is a rational number. Several examples are given, including pi/4 and 3pi/4, and sqrt(x) and sqrt(y) where x and y are both irrational and their sum is 1. The conversation also explores the possibility of adding two irrational numbers and getting a rational result, but it is concluded that this is not possible unless one of the numbers cancels out. Finally, it is stated that the difference between a rational number and an irrational number is always irrational, and this is used to prove that the sum of two irrational numbers is rational if and only if the difference between the sum and one of the irrational numbers
  • #36
When I say a random number, I mean one that can be inifinitely small to infinitely large (including number of digits) for both positive and negative numbers.
 
Physics news on Phys.org
  • #37
Jameson said:
When I say a random number, I mean one that can be inifinitely small to infinitely large (including number of digits) for both positive and negative numbers.

That doesn't tell me what you mean by random. Are all the numbers equally likely? What is the distribution?
 
  • #38
Sorry. Yes, I am saying all numbers are equally likely... I don't know what you are asking by distribution though.
 
  • #39
Jameson said:
Sorry. Yes, I am saying all numbers are equally likely... I don't know what you are asking by distribution though.

http://mathworld.wolfram.com/DistributionFunction.html

That is not possible. When you say that the numbers are equally likely then you are saying that you are using a uniform distribution. You can’t have a uniform distribution on an unbounded set
 

Similar threads

Irrational Number Raised To Irrational Number
Replies
30
Views
2K
Calc I: Limits at Infinity: Solving r Irrational
Replies
4
Views
1K
I Is the Ratio of Circumference to Radius of a Circle Always Irrational?
Replies
19
Views
2K
Spivak Thomae's Function proof explanation
2
Replies
35
Views
7K
I Are Real Numbers Essential in Scientific Measurements and Models?
3
Replies
85
Views
6K
MHB Piecewise function - rational and irrational
Replies
4
Views
8K
Irrational Numbers a and b used in various expressions
Replies
13
Views
2K
Sum of rational and irrational is irrational
Replies
6
Views
2K
I Basic measurement theory question
Replies
5
Views
2K
Spivak "root 2 is irrational number" problem
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top