query: If there a formal definition for the sum of two irrationals is rational if it is only the additive inverse plus some rational?
positive_passages.docid: 22408
positive_passages.text: Jutifying: irrational + rational = irrational
negative_passages.docid: 107105
negative_passages.text: Is an irrational number odd or even?
negative_passages.docid: 63409
negative_passages.text: If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
negative_passages.docid: 96204
negative_passages.text: Irrational number $\sqrt2$ proof
negative_passages.docid: 41486
negative_passages.text: If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
negative_passages.docid: 152512
negative_passages.text: What is the ratio of rational to irrational real numbers?
negative_passages.docid: 32
negative_passages.text: Is $n^{th}$ root of $2$ an irrational number?
negative_passages.docid: 88429
negative_passages.text: Prove $\sqrt{2} + \sqrt{5}$ is irrational
negative_passages.docid: 117366
negative_passages.text: Is there a simple, constructive, 1-1 mapping between the reals and the irrationals?
negative_passages.docid: 139979
negative_passages.text: Proof there is a rational between any two reals
negative_passages.docid: 98755
negative_passages.text: How can I show that the set of rational numbers with denominator a power of two form a dense subset of the reals?
negative_passages.docid: 48035
negative_passages.text: Prove that square root of 2 is irrational using the principle of Mathematical Induction
negative_passages.docid: 30523
negative_passages.text: A binary irrational with bits defined by primes
negative_passages.docid: 158368
negative_passages.text: Irrationals: A Group?
negative_passages.docid: 30478
negative_passages.text: How to prove that a number is irrational
negative_passages.docid: 81428
negative_passages.text: Why does proof by contradiction not work on Rational numbers but only on Irrational numbers?
negative_passages.docid: 95787
negative_passages.text: Prove or find a counterexample: For all real numbers x and y it holds that x + y is irrational if, and only if, both x and y are irrational.