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 …
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 …
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 …
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 …
Proving the area formula for a rectangle for all positive real …
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 …
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 …
Is the Square Root of Pi Irrational? - Physics Forums
Dec 14, 2012 · The proof shows that if pi is irrational then so is its square root. Presumably that is what the question asked, or intended to ask.
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 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 …
Why is Pi an irrational number? - Physics Forums
Apr 4, 2018 · The discussion centers on the nature of Pi (π) as an irrational number, emphasizing its infinite decimal expansion and its relationship to finite measurements in geometry. …