irrational = rational - Physics Forums
Mar 13, 2005 · Explore examples of irrational numbers that can be expressed as non-repeating decimals Investigate the implications of probability in selecting random real numbers Mathematicians, students …
Prove If x^2 is irrational then x is irrational - Physics Forums
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 proof. Any hint?
Proof that cube roots of 2 and 3 are irrational - Physics Forums
Jul 20, 2018 · The discussion provides a proof by contradiction demonstrating that the cube root of 2 is irrational, while the attempt to apply a similar method to the cube root of 3 fails. The proof for cube …
Showing that tan(1) is irrational - Physics Forums
Feb 11, 2019 · Homework Statement Prove that tan (1 ∘) is irrational. Homework Equations The Attempt at a Solution Suppose for contradiction that is rational. We claim that this implies that is rational. …
Irrational numbers aren't infinite. are they? - Physics Forums
Dec 28, 2016 · Irrational numbers are not infinite; they are numbers that cannot be measured precisely, with only infinite decimal approximations available. For instance, 1.41421... serves as an …
If a, b are irrational, then is - Physics Forums
Jan 13, 2017 · The discussion centers on the proposition: If a and b are irrational, then a^b is irrational. Participants explore this through proof by contradiction, using examples such as √2 and the natural …
Is Pi a rational number in any other base besides base Pi?
Jul 24, 2013 · So is an irrational number always irrational no matter what the base or is Pi just a special case? The term "irrational" is independent of what base we use. So yes, an irrational number is …
Is Planck's Constant Irrational? - Physics Forums
Sep 9, 2009 · The discussion centers on the rationality of Planck's constant, with participants debating its classification as rational or irrational. It is established that Planck's constant, defined in SI units, is …
Proving Irrationals Are Dense in the Reals • Physics Forums
Jul 29, 2010 · The discussion focuses on proving that irrational numbers are dense in the real numbers (R). The proof utilizes the property that the sum of a rational number and an irrational number is …
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, …