query: Does the set of natural numbers contain infinity?
positive_passages.docid: 158257
positive_passages.text: Is aleph-$0$ a natural number?
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: 70940
negative_passages.text: Homework - set theory infinite union
negative_passages.docid: 119982
negative_passages.text: how to express the set of natural numbers in ZFC
negative_passages.docid: 118573
negative_passages.text: Why is the Axiom of Infinity necessary?
negative_passages.docid: 59385
negative_passages.text: Are there number systems corresponding to higher cardinalities than the real numbers?
negative_passages.docid: 36281
negative_passages.text: A set is infinite iff it is equivalent to a proper subset of itself
negative_passages.docid: 124115
negative_passages.text: Give an example of a set that has the set of natural numbers as it s set of accumulation points.
negative_passages.docid: 20085
negative_passages.text: What's the cardinality of all sequences with coefficients in an infinite set?
negative_passages.docid: 132537
negative_passages.text: Class of sets of a given infinite cardinality
negative_passages.docid: 141298
negative_passages.text: Image of the set of natural numbers under any function is denumerable.
negative_passages.docid: 56233
negative_passages.text: Is the set of all strings with countably infinite length bijective to $[0,1]$?
negative_passages.docid: 156242
negative_passages.text: As many even numbers as natural numbers.
negative_passages.docid: 62348
negative_passages.text: One divided by Infinity?
negative_passages.docid: 52861
negative_passages.text: Natural Numbers and Well ordering
negative_passages.docid: 24582
negative_passages.text: Is the set of sequences of natural numbers with trailing zeros countable?
negative_passages.docid: 130542
negative_passages.text: Every natural number $n$ can be written as $n=s-t$ with $\omega(s)=\omega(t)$