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 + …

Jan 12, 2022 · A polynomial can indeed have irrational coefficients, as demonstrated by the example y = x^2 + sqrt (5)x + 1. The confusion arises from historical conventions where coefficients were often …

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 numbers like …

Dec 28, 2016 · There are an infinite number of irrational numbers just as there are an infinite number of integers, rational numbers and real numbers. However since reals are uncountable and rationals are …

Oct 13, 2025 · The Attempt at a Solution By contradiction: Prove that when an irrational number is divided by a nonzero rational number, the resulting number is rational.

Feb 23, 2012 · The discussion revolves around proving that the square root of an irrational number is also irrational. Participants suggest using proof by contradiction, where assuming the square root is …

Nov 18, 2003 · Not all irrational numbers can be expressed as infinite summations, as there are uncountably many irrational numbers but only countably many mathematical expressions. While any …

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 considered …

Aug 29, 2005 · Ok so I am to prove: If x is irrational, then \sqrt {x} is irrational. So I started by trying to prove the contrapositive: If \sqrt {x} is rational, then x is rational.

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 irrationality …