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 …
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 …
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 …
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 …
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 …
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.
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 …