Irrational Definition and 349 Threads

... can we convert this equation to binary notation? Also another one, would an irrational number be irrational in any number format?

Show that the equation 4x^(2) + 5y^(2) = 2 has no rational solutions. Can this be done graphically?

Homework Statement Prove by contradiction: If a and b are rational numbers and b != 0, and r is an irrational number, then a+br is irrational. In addition, I am to use only properties of integers, the definitions of rational and irrational numbers, and algebra. You guys should also know that...

Give an example of a function f:(0,1)-->Reals which is continuous at exactly the irrational points in (0,1). I think the function f such that f(x)=1/n if x is rational in (0,1) (x=m/n for some n not 0) and f(x)= 0 if x is irrational in (0,1) should work. I get the reason why f is continuous...

Homework Statement Let x be an irrational number. Show that the absolute value of the difference between jx and the nearest integer to jx is less than 1/n for some positive integer j not exceeding n. Homework Equations The Attempt at a Solution Ok, I know that it should be solved using...

Homework Statement Prove that there exists an irrational between any two rationals. Homework Equations The Attempt at a Solution How would one do this? So far I've proven there is an irrational between any rational and irrational, any irrational and rational, that there's a...

How do you show that the cubic root of two + the square root of two is irrational? I can easily show that each of these numbers is irrational, but not the sum :/.

Hello. Between a rational and a irrational is there a rational? and a irrational? and vice-versa? I know that between 2 rationals there is a rational and a irrational and that between 2 irrationals there is a rational and a irrational, but i cannot figure this out... please help. Thanks.

Homework Statement Prove that if x^2 is irrational then x must be irrational. Homework Equations The Attempt at a Solution Maybe do proof by contradiction. I'm not really sure where to start.

Homework Statement prove that it is possible that an irrational number raised to another irrational, can be rational. you are given root2 to root2 to root2 Homework Equations The Attempt at a Solution i have shown that root2 to root2 to root2 is rational, but would appreciate a...

Question: Using the fact that \sqrt{2} is irrational, we can actually come up with some interesting facts about other numbers. Consider the number t=1/\sqrt{2}, which is also irrational. Let a and b be positive integers, and a<b. We will prove that any rational approximation a/b of t will...

hi well I'm having truple in proving this (sqrt(2))^3 is irrational number!

How do we exactly define irrational numbers.. ive asked this before... but id like to know about any infinite series, if any which is used to define irrational numbers... and how can one prove properties of basic operations for irrational numbers Thanks

Hello everyone! I was wondering.. if you could help me calculate some integrals: It's not for Homework or something, just my curiosity: \displaystyle{\int}\sqrt[3]{x^2-1} dx What would you suggest? I tried substitution, thou it seems to me useless. Are these integrals common in...

i.e. decimals of an irrational number, pi(n), etc. The function itself, f(n), can change with n, as long as it changes in a patterned way. This seems like a straight foreword question, either you can for all, or you can't for all. A simple example of a changing function would be the...

I've been thinkng about this one for a while. Is i rational or irrational. i is an imaginary number, so logically, it would be irrational. But \frac{-1}{i} = i so it has a fractional equivilant. But then, it doesn't have a real number decimal equivilant... So, what is it? Is i rational or...

and, consequently, infinitely many. I am new to proofs so could you please check if this proof is correct? Let x be an irrational number in the interval I[SIZE="1"]n = [a[SIZE="1"]n, b[SIZE="1"]n], where a[SIZE="1"]n and b[SIZE="1"]n are both rational numbers, in the form p/q. Let z be...

I know this will sound nuts, because it kind of is, but I though maybe someone could talk some sense into me. I suffer from ocd and irrational fears about radioactive substances. I realize that we are surrounded by and constantly bombarded by radiation. That doesn't bother me. Nor does having...

1st I assume it is rational so: 7^(1/7) = m/n then 7 = (m^7)/(n^7) implies m^7 is a multiple of 7. Means m^7 = 0 mod 7 So, using fermats little theorem.. m^7 = m mod 7 for m to be in the class of 0 it has to be a multiple of 7. Now set m = 7k, so 7n^7 = 49k^7 But...

Hey, Homework Statement (From an Integration Table) Prove, {\int}{\sqrt {{{a}^{2}} - {{x}^{2}}}}{dx} = {{\frac {1}{2}}{\left(}{{{x}{\sqrt {{{a}^{2}} - {{x}^{2}}}}} + {{{a}^{2}}{\arcsin{\frac {x}{a}}}}}{\right)}}{,}{\,}{\,}{\,}{\,}{\,}{\,}{{{|}{x}{|}}{\leq}{{|}{a}{|}}} Homework...

[SOLVED] continuous at irrational points Homework Statement Every rational x can be written in the form m/n where n>0, and m and n are integers without any common divisors. When x = 0, we take n=1. Consider the function f defined on the reals by f(x) = 0 if x is irrational and f(x) = 1/n if x...

Can someone pls help me on "rational and Irrational numbers". Esp. on Decimals. I can't classify if it is rational or irrational.

I've started to work on the it, just tell me if I'm on the right track. cos (45-30) = (\sqrt{3} + 1) / 2\sqrt{2} so cos 15 is irrational. cos3x = 4cos^3x - 3cos x \Rightarrow cos 5 is irrational cos 4x... cos 20 If this is a bad way, maybe someone knows a better one. Here is what I think...

Here is the scenario. Picture three people standing at a playground watching the children play. The first is grouchy and sees all the busy activity as stressful noise. The second person is in a good mood and sees the child play as relaxing and fun. The third person is full of anxiety and sees...

I want to prove that \sqrt 6 - \sqrt 2- \sqrt 3 is irrational. I already know that \sqrt 2+\sqrt 3 is irrational (by squaring it). I would like a proof that doesn't use a polynomial and the rational root theorem. Thanks.

wat are the answers for these in terms of rational,irrational (irrational number)*(any +ve integer) = ? (any +ve integer) - (irrational number)*(any integer) = ? are the answers also irrational numbers

I know that √2 is irrational (and I've seen the proof). Now, what is the fastest way to justify that 2√2, 2-√2, 17√(1/2)[/color] are irrational? (they definitely "seem" to be irrational numbers to me) Can all/any these follow immediately from the fact that √2 is irrational? Thanks!

[SOLVED] Prove that the cuberoot of 2 is irrational Homework Statement Prove that the cuberoot of 2 is irrational The Attempt at a Solution Assume it is rational, and find a contradiction. 2^(1/3) = a/b, where a, b are integers, where a/b is in lowest terms, and where b != 0. 2 = a^3 /...

Hi, does somebody know an example of two surds that, added together, give another surd? By 'surd' I mean here 'irrational surd', as opposed to \sqrt 4 + \sqrt 9 = \sqrt 25.

Homework Statement Prove, for every L which is in the real number system, there exists a sequence (qn)which is a proper subset of the irrationals such that the limit as n approaches infinity of qn=L

http://web01.shu.edu/projects/reals/infinity/irrat_nm.html Well there is the proof i am reading and trying to understand... can someone tell me how they knew that 0<R_n<\frac{3}{(n+1)!}

Homework Statement Prove that log2 of 5 is irrational. Homework Equations None. The Attempt at a Solution I just had a glimpse of the actual solution, but I'm wondering if mine would work too. 2^(a/b) = 5 square both sides... 2^(2a/b) =25 2 = 25^(b/2a) (b/2a) = log25 of 2 b =...

limit proof?? well what i am trying to understand,actually proof is if we can get with the limit inside a power (exponent) if the exponent is irrational. Say we have any sequence (a_n) or any function f(x), let p be irrational then can we do the following, if yes why, if not why? 1...

what's the polynomial equation which sqrt2 + sqrt3 satisfies ?

hi i m hashim i want to solve a qquestion 1.if x is rational & y is irrational proof x+y is irrational? 2. if x not equal to zero...y irrational proof x\y is irrational?? 3.if x,y is irrational ..dose it implise to x+y is irrational or x*y is irrational thanks please hashim

The golden ratio is irrational. Do you know any clever proofs for this fact? I put this here, because it's not homework--only more of a discussion.

Homework Statement For the following irrational equation x^2 + 7x + 10 + \sqrt{x^2 + 7x + 12} = 0 Find all possible unknown of X. Homework Equations None. Just your ability to solve equations. The Attempt at a Solution First of all, I am not allowed to use a calculator to...

Hi guys, How would you prove that \sqrt[3]{7} is irrational without using the unique factorization thrm? I tried proving that \sqrt[3]{7} is rational but it didn't seem to get me anywhere... Thanks EDIT: Looks like I posted this in the wrong forum.

Homework Statement Let n and k be positive integers. Show that k^{1/n} is either a positive integer or an irrational number. The Attempt at a Solution I set q = k^{1/n}. Then I set q = \frac{m}{p} . (Where m and p don't have common factors.) Then m^n = k * p^n . So then k is a factor...

This isn't really a question about homework specifically, it's more just that I don't understand part of my chapter...I am just starting Principles of Mathematical Analysis by Ruben... Here is what I don't understand: It is proving that p^2 = 2 is not satisfied by any rational p. And it...

Hello, here is my problem: how can i prove that if a\in\mathbf{Q} and t\in\mathbf{I}, then a+t\in\mathbf{I} and at\in\mathbf{I}? My original thought was to show that neither a+t or at can be belong to N, Z, or Q, thus they must belong to I. However I'm not certain if that train of thought...

I wish to prove that for f(x)=x^x, its domain is: {x E R, x > 0}U{xEZ,x<0}. I reevaluated to e^(xlnx), obviously that did not help. Is there an algorithm/formula/something that can evaluate irrational powers, so that it can help me with this?

Homework Statement How are you able to determine if a solution is rational or irrational Homework Equations - The Attempt at a Solution - :confused: I'm pretty sure it will be something basic I'm forgetting, thanks for any help.

Homework Statement the indefinite integral of (1+lnx)^(1/2)/(xlnx) dx Homework Equations n/a The Attempt at a Solution There aren't any x^2 in the root sign, so I don't think it can be a trig substitution. The only logical u sub I see is to let u=lnx. In that case, du=dx/x so the...

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Im wondering if its possible given x,y irrational, that x-y is rational (other than the case x=y). The reason I am asking this is that I am reading a book on measure theory and they try to construct a non measurable set and they start with an equivalence relation on [0,1} x~y if x-y is rational...

Homework Statement Prove 5^{1/3} - 3^{1/4} is irrational. Homework Equations http://www.purplemath.com/modules/solvpoly.htm The Attempt at a Solution Ok, what I have tried doing is using the about Rational Roots property by letting x = 5^{1/3} - 3^{1/4} and trying to pull out a...

How random are the digits of irrational numbers? Can it be said of them (i.e. pi=3.14159...) that given any arbitrarily long string of digits it must occur at some point in any irrational number? And would anyone know of anywhere I could find out more on this topic?

i know what the meaning of a^p is when p is an integer or rational. e.g., a^3 = a.a.a or a^{\frac{1}{5}} is such a number that when multiplied five times gives the number a. but what is the menaing of a^p when p is an irrational number?

I have discovered the mighty blade of Occam, I shall destroy all who advocate the existence of irratonal numbers. [SIZE="1"]Spiders are your gods.