Oct 13, 2025 · Dividing an irrational number by a nonzero rational number results in an irrational number. The proof by contradiction assumes that the result is rational, leading to the …

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 …

Mar 25, 2014 · The discussion centers on the nature of irrational and transcendental numbers, specifically whether they can have repeating decimal expansions. It is established that …

Dec 6, 2004 · The discussion centers on the nature of irrational numbers and their existence in the physical world, questioning how lengths like the hypotenuse of a right triangle can be …

Jan 25, 2019 · The discussion centers on proving or disproving the existence of a rational number x and an irrational number y such that x^y is irrational. Participants suggest that proof by …

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 …

Jun 26, 2008 · Is there always at least one irrational number between any two rational numbers? JG89 Jun 26, 2008 Irrational Irrational number Numbers Rational Click For Summary

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.

Mar 16, 2016 · The discussion centers on the relationship between irrational numbers and the measurement of physical quantities. It highlights that while irrational numbers, such as the …

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 …