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.
 
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  • #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
 

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