Mar 13, 2005 · Assume that the difference between a rational number and an irrational number is an irrational number. The sum of any such two irrational numbers would be a rational number.

Dec 28, 2016 · While decimal representations of irrational numbers are non-repeating and infinite, there are indeed an infinite number of irrational numbers, which are uncountable compared to …

Aug 1, 2012 · Does anyone know if it has ever been proved that pi divided e, added to e, or any other mathematical operation combining these two irrational numbers is rational. Another thing …

Feb 17, 2010 · Irrational numbers have practical applications in real life, such as calculating dimensions for circular objects, like the border of a circular card, which involves pi. The …

Apr 26, 2012 · The discussion centers on proving that the expression a + (1/√2) (b-a) is irrational when a and b are distinct rational numbers. Participants analyze the algebraic steps taken to …

Sep 13, 2003 · The discussion centers on whether the ratio of two irrational numbers can be rational. It establishes that while any irrational number multiplied by a nonzero integer remains …

Oct 23, 2012 · The problem reads as follows: Let n be a positive integer that is not a perfect square. Prove that √n is irrational. I understand the basic outline that a proof would have. …

Jul 24, 2013 · Pi is irrational in any base, as its property of being rational is independent of the base used for representation. While it can be expressed differently in various bases, such as …

Mar 14, 2005 · This method produces rational approximations that converge quickly to the irrational number. Additionally, the continued fraction representation of the square root of 2 …

Mar 8, 2004 · Irrational numbers cannot be expressed as fractions, while transcendental numbers are not solutions to any polynomial equations with rational coefficients. For example, \ (\sqrt …