Mar 13, 2005 · One participant proposes a general case involving the difference between a rational number and an irrational number being irrational, suggesting this leads to the conclusion that 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 same proof …

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. Assume √n is …

Jun 17, 2021 · Can an irrational number raised to an irrational power yield an answer that is rational? This problem shows that the answer is “yes.” (However, if you study the following solution very …

Nov 18, 2003 · The discussion centers around whether all irrational numbers can be expressed as infinite summations, similar to well-known constants like Pi and e. Participants explore the …

Jul 24, 2013 · There is a discussion about whether an irrational number could appear rational in another base, specifically mentioning that Pi in base Pi is represented as 10. Some participants explore the …

Mar 8, 2004 · The discussion centers on the distinctions and relationships between irrational numbers and transcendental numbers, exploring definitions, examples, and implications within mathematical …

May 8, 2014 · The discussion centers on proving that \ (\sqrt {6}\) is an irrational number. The proof begins by assuming \ (\sqrt {6}\) can be expressed as a ratio of two integers, leading to a …

Dec 28, 2016 · The discussion revolves around the nature of irrational numbers, specifically questioning whether they are infinite or merely unmeasurable. Participants explore the concept of irrational …

Feb 17, 2010 · The discussion revolves around the real-life applications of irrational numbers, exploring their relevance and implications in various contexts, including mathematics, carpentry, and …