query: How do mathematicians think about arbitrary elements?
positive_passages.docid: 146260
positive_passages.text: Question about how to interpret arbitrary elements
negative_passages.docid: 26724
negative_passages.text: Mathematician learning theoretical physics
negative_passages.docid: 49157
negative_passages.text: First order theory - define a domain with an even number of elements
negative_passages.docid: 125174
negative_passages.text: Combinatorial intuition of identity
negative_passages.docid: 118130
negative_passages.text: Mathematical notation around the world
negative_passages.docid: 55432
negative_passages.text: Infinite distinct factorizations into irreducibles for an element
negative_passages.docid: 67578
negative_passages.text: Is this a correct demonstration for why elements above untriseptium cannot exist?
negative_passages.docid: 147924
negative_passages.text: Math problems that are impossible to solve
negative_passages.docid: 74875
negative_passages.text: Do we know if there exist true mathematical statements that can not be proven?
negative_passages.docid: 22498
negative_passages.text: In set theory, how are real numbers represented as sets?
negative_passages.docid: 89989
negative_passages.text: A set of integers whose elements all divide $2015^{200}$ but do not divide each other
negative_passages.docid: 47845
negative_passages.text: Mirror algorithm for computing $\pi$ and $e$ - does it hint on some connection between them?
negative_passages.docid: 30625
negative_passages.text: Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers
negative_passages.docid: 70332
negative_passages.text: Is there a third dimension of numbers?
negative_passages.docid: 108922
negative_passages.text: Cardinality and infinite sets: naturals, integers, rationals, bijections
negative_passages.docid: 106211
negative_passages.text: Is the universe isomorphic to a universal turing machine?
negative_passages.docid: 12433
negative_passages.text: How do $\pi^0$ particles exist?