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 …
Is Dividing an Irrational Number by a Rational Number Always …
Nov 10, 2025 · Dividing an irrational number by a nonzero rational number results in an irrational number. The proof by contradiction assumes that the result is rational, leading to the conclusion that …
Is the square root of a prime number always going to be irrational?
Sep 2, 2006 · In general, I think that the nth root of any natural number that is not itself a perfect nth power is an irrational number. This is true, and in fact the nth root of any rational number which …
Showing that tan(1) is irrational - Physics Forums
Feb 11, 2019 · The discussion centers on proving that is irrational through a proof by contradiction and mathematical induction. It establishes that if is rational, then must also be rational for all natural …
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 …
Constructing Lengths with Irrational Numbers - Physics Forums
Dec 6, 2004 · Irrational numbers are just an inconsistent fabrication of abstract mathematics. Irrational lengths can't exist in the real world. And rational lengths can ? There is no way that you are going to …
Prove or disprove that there is a rational number x and an i
Jan 25, 2019 · The discussion centers on proving or disproving the existence of a rational number x and an irrational number y such that x^y is irrational. Participants suggest that proof by contradiction is a …
How Can Rational and Irrational Numbers Combine in Arithmetic ...
May 14, 2017 · This discussion focuses on the arithmetic operations involving irrational numbers, specifically how certain combinations can yield rational or irrational results. Examples provided …
Can a polynomial have an irrational coefficient? - Physics Forums
Jan 12, 2022 · The discussion clarifies that a polynomial can indeed have irrational coefficients, as demonstrated by the example y = x² + √5x + 1. The misconception that coefficients must be rational …
How did the Greeks deal with sqrt (2)? • Physics Forums
Dec 21, 2018 · SUMMARY The ancient Greeks, particularly the Pythagoreans, recognized the existence of irrational numbers, exemplified by the proof of the irrationality of 2 attributed to Hippasus. Despite …