query: What is a property that looks like it holds for all natural numbers but it turns out it doesn't?
positive_passages.docid: 5574
positive_passages.text: Conjectures that have been disproved with extremely large counterexamples?
negative_passages.docid: 13363
negative_passages.text: Why does an argument similiar to 0.999...=1 show 999...=-1?
negative_passages.docid: 32708
negative_passages.text: Showing Intermediate Value Property Holds
negative_passages.docid: 31392
negative_passages.text: Examples and Counterexamples of Relations which Satisfy Certain Properties
negative_passages.docid: 80320
negative_passages.text: When can I assume that all decimal digits returned by Mathematica are provably correct?
negative_passages.docid: 5375
negative_passages.text: Is there a bijective function mapping Natural numbers to Natural numbers, other than $f(n) = n$?
negative_passages.docid: 90952
negative_passages.text: Does every number not ending with zero have a multiple without zero digits at all?
negative_passages.docid: 151521
negative_passages.text: Set Theory: Tree Property
negative_passages.docid: 24582
negative_passages.text: Is the set of sequences of natural numbers with trailing zeros countable?
negative_passages.docid: 119982
negative_passages.text: how to express the set of natural numbers in ZFC
negative_passages.docid: 43024
negative_passages.text: Well-ordered sets, properties of an element that is not largest in the set
negative_passages.docid: 82739
negative_passages.text: Why is $\alpha \rightarrow \forall x(\alpha)$ not generally correct in first-order logic?
negative_passages.docid: 114650
negative_passages.text: In Cantor's Diagonalization Argument, why are you allowed to assume you have a bijection from naturals to rationals but not from naturals to reals?
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: 156242
negative_passages.text: As many even numbers as natural numbers.
negative_passages.docid: 25874
negative_passages.text: Showing that a certain map is not flat by explicit counterexample
negative_passages.docid: 72420
negative_passages.text: Is $\mathbb{N}$ impossible to pin down?