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.

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 …

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 …

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 …

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 …

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 …

Jun 26, 2008 · But again, an irrational number plus a rational number is also irrational. Therefore, there is always at least one rational number between any two rational numbers. However, the …

Jul 29, 2010 · Homework Statement Show that the irrational numbers are dense in R. [Hint: Use the fact that sqrt(2) is irrational.]Homework Equations Book already proved that the rationals …

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 …

Jan 6, 2012 · Homework Statement Prove If x^2 is irrational then x is irrational. I can find for example π^2 which is irrational and then π is irrational but I don't know how to approach the …