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 …
Is a + (1/√2) (b-a) Irrational? - Physics Forums
Apr 26, 2012 · Homework Statement Prove that if a and b are rational numbers with a≠b then a+ (1/√2) (b-a) is irrational. Homework Equations The Attempt...
If a, b are irrational, then is - Physics Forums
Jan 13, 2017 · Homework Statement True or false and why: If a and b are irrational, then ##a^b## is irrational. Homework Equations None, but the relevant example provided in the text is the …
Showing that tan(1) is irrational - Physics Forums
Feb 11, 2019 · Homework Statement Prove that ##\tan (1^\circ)## is irrational. Homework EquationsThe Attempt at a Solution Suppose for contradiction that ##\tan...
Prove If x^2 is irrational then x is irrational - Physics Forums
Jan 6, 2012 · Homework Statement Prove If x^2 is irrational then x is irrational. I can find for example π^2 which is irrational and then π is irrational but I don't know how to approach the …
Irrational numbers vs. Transcendental numbers - Physics Forums
Mar 8, 2004 · It would seem that an irrational number would have to be a transcendental number. If a transcendental number is a number which goes on infinitely and never repeats, then all …
Irrational Flow yields dense orbits. - Physics Forums
Mar 19, 2012 · I have the folloring problem: Given the following flow on the torus (θ_1)' = ω_1 and (θ_2)' = ω_2, where ω_1 /ω_2 is irrational then I am asked to show that each trajectory is …
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 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
Proving Irrationals Are Dense in the Reals • Physics Forums
Jul 29, 2010 · Homework Statement Show that the irrational numbers are dense in R. [Hint: Use the fact that sqrt(2) is irrational.]Homework Equations Book already proved that the rationals …