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 a + (1/√2)(b-a) Irrational? - Physics Forums
Apr 26, 2012 · The discussion centers on proving that if \ ( a \) and \ ( b \) are rational numbers with \ ( a \neq b \), then \ ( a + \frac {1} {\sqrt {2}} (b-a) \) is irrational. Participants analyze the algebraic steps …
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 …
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. …
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 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 …
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 …
Why are there more irrational numbers than rational numbers?
Sep 8, 2004 · The discussion clarifies that there are more irrational numbers than rational numbers due to the concept of cardinality, as established by Georg Cantor's Diagonalization argument. The …
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 …
Irrational Numbers and Real Life I need 6 answers - Physics Forums
Feb 17, 2010 · This discussion centers on the real-life applications of irrational numbers, specifically highlighting their relevance in geometry and finance. Examples include calculating the circumference …