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 …
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: Expressible as Infinite Summations?
Nov 18, 2003 · All irrational numbers can be expressed as infinite summations, but not all can be uniquely represented by mathematical expressions. For example, while Pi (π) and the natural …
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?
Calculus of Measures: Mapping Natural Numbers to Rationals
Jun 2, 2018 · The discussion centers on the mapping of natural numbers to positive rationals and the implications of measure theory on their densities. It is established that both the set of rational …
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 …
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 …
Is there a Whole Number Multiple of Pi Closest to a Whole Number ...
Sep 16, 2012 · The discussion centers on the question of whether a whole number multiple of π can be found that is closest to a whole number. It is established that no single whole number multiple exists …
Proving the area formula for a rectangle for all positive real numbers ...
Aug 3, 2024 · The area formula for a rectangle, defined as length times width, holds true for all positive real numbers, including rational and irrational values. The discussion emphasizes the need for an …
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, …