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 …
How Do We Know If Irrational or Transcendental Numbers Repeat?
Mar 25, 2014 · The discussion revolves around the nature of irrational and transcendental numbers, specifically whether their decimal expansions can repeat. Participants explore the implications of …
Constructing Lengths with Irrational Numbers - Physics Forums
Dec 6, 2004 · The discussion revolves around the construction of lengths that are irrational numbers, particularly in the context of geometric figures like right triangles and circles. Participants explore the …
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 …
Proving √n Irrational: A Proof by Contradiction - Physics Forums
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 …
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 …
Irrational Number Raised To Irrational Number - Physics Forums
Jun 17, 2021 · The discussion revolves around whether an irrational number raised to an irrational power can yield a rational result. The original poster presents a specific case involving \ ( A = (\sqrt …
Showing that tan(1) is irrational - Physics Forums
Feb 11, 2019 · (1 ∘) is irrational. Homework Equations The Attempt at a Solution Suppose for contradiction that is rational. We claim that this implies that is rational. Here is the proof by induction: …
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. …
Irrational numbers vs. Transcendental numbers - Physics Forums
Mar 8, 2004 · The discussion centers on the distinctions and relationships between irrational numbers and transcendental numbers, exploring definitions, examples, and implications within mathematical …