irrational = rational - Physics Forums
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 …
Proving √n Irrational: A Proof by Contradiction - Physics Forums
Oct 23, 2012 · The discussion focuses on proving that the square root of a non-perfect square integer \ ( n \) is irrational using a proof by contradiction. The proof begins by assuming \ ( \sqrt {n} \) is rational, …
Irrational Number Raised To Irrational Number - Physics Forums
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 …
Is there always at least one irrational number between any two rational ...
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 …
Irrational Numbers: Expressible as Infinite Summations?
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 …
Irrational numbers aren't infinite. are they? - Physics Forums
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 …
Proof that cube roots of 2 and 3 are irrational - Physics Forums
Jul 20, 2018 · The discussion revolves around the proof of the irrationality of the cube roots of 2 and 3, focusing on various approaches and the challenges encountered in establishing these proofs. …
Why are there more irrational numbers than rational numbers?
Sep 8, 2004 · One participant suggests that there are infinitely many irrational numbers between any two rational numbers, although another points out that the listed examples were rational. Another …
Is Pi divided by E rational, and what other irrational numbers exist ...
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 does …
Irrational Numbers and Real Life I need 6 answers - Physics Forums
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 …