query: Are there theorems in number theory which are true for a large interval, but are known to be false for an arbitrarily large number outside that range?
positive_passages.docid: 29142
positive_passages.text: Examples of patterns that eventually fail
negative_passages.docid: 138446
negative_passages.text: Proving that there exists an irrational number in between any given real numbers
negative_passages.docid: 2402
negative_passages.text: Does $\sin n$ have a maximum value for natural number $n$?
negative_passages.docid: 153033
negative_passages.text: Is something similar to Robin's theorem known for possible exceptions to Lagarias' inequality?
negative_passages.docid: 80920
negative_passages.text: Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
negative_passages.docid: 93805
negative_passages.text: Is there a good (preferably comprehensive) list of which conjectures imply the Riemann Hypothesis?
negative_passages.docid: 155112
negative_passages.text: Are there more rational numbers than integers?
negative_passages.docid: 71058
negative_passages.text: Is there a value of the function $g$ that is greater than the length of the interval?
negative_passages.docid: 111723
negative_passages.text: Can it be proven in $\sf ZF^{\neg\infty}$ that the sets $x_n=\{x_{n+1}\}$ do not exist?
negative_passages.docid: 6396
negative_passages.text: If two limits don't exist, are we sure the limit of sum doesn't exist?
negative_passages.docid: 103581
negative_passages.text: Which positive integers can NOT be written as a sum of consecutive positive integers
negative_passages.docid: 69838
negative_passages.text: Does a countably infinite power set exist?
negative_passages.docid: 109305
negative_passages.text: Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
negative_passages.docid: 73612
negative_passages.text: Is there a Non-prime Number that is Divisible only by Numbers Greater than its Square Root?
negative_passages.docid: 150917
negative_passages.text: Show that $\lim_{n\to \infty}\sin{n\pi x} =0$ if $x\in \mathbb{Z},$ but the limit fails to exist if $x\notin \mathbb{Z}.$
negative_passages.docid: 53525
negative_passages.text: Infiniteness of non-twin primes.
negative_passages.docid: 126015
negative_passages.text: Elementary number theory in sets