Mar 13, 2005 · The discussion centers on whether two irrational numbers can sum to a rational number, with examples provided such as (1 - π) + π = 1, demonstrating that this is indeed …

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 …

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 …

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 …

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 …

Jul 29, 2010 · The discussion focuses on proving that irrational numbers are dense in the real numbers, starting from the established fact that rational numbers are dense in R. The initial …

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 …

Jul 20, 2018 · Proof by contradiction that cube root of 2 is irrational: Assume cube root of 2 is equal to a/b where a, b are integers of an improper fraction in its...

Apr 30, 2010 · There is no smallest positive irrational number, as demonstrated through proof by contradiction. By assuming the existence of a smallest positive irrational number, one can …

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. …