Is Dividing an Irrational Number by a Rational Number Always …
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 …
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 …
Is it possible to define irrational powers for negative numbers?
Oct 17, 2010 · The discussion revolves around the challenges of defining irrational powers for negative numbers, particularly in the context of the function y=x^ (1/x). It is noted that while …
How Do We Know If Irrational or Transcendental Numbers Repeat?
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 …
Constructing Lengths with Irrational Numbers - Physics Forums
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 …
Why is Pi an irrational number? • Physics Forums
Apr 4, 2018 · Pi is an irrational number because it cannot be expressed as a fraction of two integers, despite being the ratio of a circle's circumference to its diameter. The confusion …
Prove or disprove that there is a rational number x and an i
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 …
Showing that tan(1) is irrational - Physics Forums
Feb 11, 2019 · Homework Statement Prove that ##\tan (1^\circ)## is irrational. Homework EquationsThe Attempt at a Solution Suppose for contradiction that ##\tan...
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 …
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.