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.

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 …

Feb 11, 2019 · Homework Statement Prove that tan (1 ∘) is irrational. Homework Equations The Attempt at a Solution Suppose for contradiction that tan (1 ∘) is rational. We claim that this …

Jul 20, 2018 · The discussion centers on proving the irrationality of the cube roots of 2 and 3. The proof for the cube root of 2 uses a contradiction approach, showing that assuming it can be …

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 …

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 …

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 …

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 …

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 …