Is Dividing an Irrational Number by a Rational Number Always …
Oct 13, 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 …
F(x) = x if x is rational, 0 if x is irrational. - Physics Forums
Oct 4, 2011 · Homework Statement F (x) = x if x is rational, 0 if x is irrational. Use the δ, ε definition of the limit to prove that lim (x→0)f (x)=0. Use the δ, ε...
irrational = rational - Physics Forums
Mar 13, 2005 · Can someone prove that there exists x and y which are elements of the reals such that x and y are irrational but x+y is rational? Certainly, there are an infinite number of …
The Pauli-Villars regularization method is a technical improvement on the primitive cutoff regularization scheme we have used so far. For example, since momentum integrals now run …
Sequence of rationals converging to an irrational limit
Aug 23, 2009 · As another illustration, I understand that if a sequence (s_n) given as s_n = \sqrt {2} + 1/n is a sequence of IRRATIONAL numbers converging to an IRRATIONAL limit.
How did the Greeks deal with sqrt(2)? • Physics Forums
Dec 21, 2018 · The Greeks recognized the existence of irrational numbers, such as √2, but struggled with their implications due to their philosophical beliefs that all numbers should be …
Is sqrt(5) Rational? Understanding the Proof by Contradiction
Nov 23, 2003 · Alright, heading says it all. This is a nice problem heh.. I can see how to prove sqrt(5) is irrational. I think this method works up to the points where the fact 5 is a prime is …
Constructing Lengths with Irrational Numbers - Physics Forums
Dec 6, 2004 · The discussion centers on the nature of irrational numbers and their existence in the physical world, questioning how lengths like the hypotenuse of a right triangle can be …
Irrational numbers aren't infinite. are they? • Physics Forums
Dec 28, 2016 · I Irrational numbers aren't infinite. are they? CollinsArg Dec 28, 2016 Infinite Irrational Irrational numbers Numbers Pi
Irrational Numbers and Real Life I need 6 answers - Physics Forums
Feb 17, 2010 · Irrational Numbers and Real Life I need 6 answers jmlink Feb 17, 2010 Irrational Irrational numbers Life Numbers Click For Summary