irrational = rational - Physics Forums
Mar 13, 2005 · Can someone prove that there exists x and y which are elements of the reals such that x and y are irrational but x+y is rational? Certainly, there are an infinite number of examples (pi/4 + …
Is a + (1/√2) (b-a) Irrational? - Physics Forums
Apr 26, 2012 · It is "fair to say that \sqrt {2} is irrational" if that has already been proven. If not, as I said, it is easier to prove than this number, using the same ideas as you did: if \sqrt {2} were rational, we …
If a, b are irrational, then is - Physics Forums
Jan 13, 2017 · Homework Statement True or false and why: If a and b are irrational, then ##a^b## is irrational. Homework Equations None, but the relevant example provided in the text is the proof of …
How did the Greeks deal with sqrt(2)? • Physics Forums
Dec 21, 2018 · The Greeks recognized the existence of irrational numbers, such as √2, but struggled with their implications due to their philosophical beliefs that all numbers should be expressible as …
Is sqrt(5) Rational? Understanding the Proof by Contradiction
Nov 23, 2003 · Alright, heading says it all. This is a nice problem heh.. I can see how to prove sqrt(5) is irrational. I think this method works up to the points where the fact 5 is a prime is used, (ie prime …
Proving Irrationals Are Dense in the Reals • Physics Forums
Jul 29, 2010 · Homework Statement Show that the irrational numbers are dense in R. [Hint: Use the fact that sqrt(2) is irrational.]Homework Equations Book already proved that the rationals are dense in …
Proof that sqrt(6)-sqrt(2)-sqrt(3) is irrational - Physics Forums
Mar 21, 2008 · The discussion focuses on proving that the expression √6 - √2 - √3 is irrational without using polynomials or the rational root theorem. Participants explore various approaches, including …
Constructing Lengths with Irrational Numbers - Physics Forums
Dec 6, 2004 · Irrational numbers are just an inconsistent fabrication of abstract mathematics. Irrational lengths can't exist in the real world. And rational lengths can ? There is no way that you are going to …
What is the Sum of Two Irrational Numbers? - Physics Forums
Feb 14, 2005 · 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 …
Sequence of rationals converging to an irrational limit
Aug 23, 2009 · As another illustration, I understand that if a sequence (s_n) given as s_n = \sqrt {2} + 1/n is a sequence of IRRATIONAL numbers converging to an IRRATIONAL limit.